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Shielding gas
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Shielding gases are inert or semi-inert gases that are commonly used in several welding processes, most notably gas metal arc welding and gas tungsten arc welding (GMAW and GTAW, more popularly known as MIG and TIG, respectively). Their purpose is to protect the weld area from oxygen, and water vapour. Depending on the materials being welded, these atmospheric gases can reduce the quality of the weld or make the welding more difficult. Other arc welding processes use other methods of protecting the weld from the atmosphere as well – shielded metal arc welding, for example, uses an electrode covered in a flux that produces carbon dioxide when consumed, a semi-inert gas that is an acceptable shielding gas for welding steel.
Improper choice of a welding gas can lead to a porous and weak weld, or to excessive spatter; the latter, while not affecting the weld itself, causes loss of productivity due to the labor needed to remove the scattered drops.
Contents
[hide]
1 Common shielding gases
2 Properties
2.1 Common mixes
3 Applications
4 See also
5 External links
6 References
Common shielding gases[edit]
Shielding gases fall into two categories—inert or semi-inert. Only two of the noble gases, helium and argon, are cost effective enough to be used in welding. These inert gases are used in gas tungsten arc welding, and also in gas metal arc welding for the welding of non-ferrous metals. Semi-inert shielding gases, or active shield gases, include carbon dioxide, oxygen, nitrogen, and hydrogen. These active gases are used with GMAW on ferrous metals. Most of these gases, in large quantities, would damage the weld, but when used in small, controlled quantities, can improve weld characteristics.
Properties[edit]
The important properties of shielding gases are their thermal conductivity and heat transfer properties, their density relative to air, and the ease with which they undergo ionization. Gases heavier than air (e.g. argon) blanket the weld and require lower flow rates than gases lighter than air (e.g. helium). Heat transfer is important for heating the weld around the arc. Ionizability influences how easy the arc starts, and how high voltage is required. Shielding gases can be used pure, or as a blend of two or three gases.[1][2] In laser welding, the shielding gas has an additional role, preventing formation of a cloud of plasma above the weld, absorbing significant fraction of the laser energy. This is important for CO2 lasers; Nd:YAG lasers show lower tendency to form such plasma. Helium plays this role best due to its high ionization potential; the gas can absorb high amount of energy before becoming ionized.
Argon is the common shielding gas, widely used as the base for the more specialized gas mixes.[3]
Carbon dioxide is the least expensive shielding gas, providing deep penetration, however it negatively affects the stability of the arc and enhances the molten metal's tendency to create droplets (spatter).[4] Carbon dioxide in concentration of 1-2% is commonly used in the mix with argon to reduce the surface tension of the molten metal. Another common blend is 25% carbon dioxide and 75% argon for GMAW.[5]
Helium is lighter than air; larger flow rates are required. It is an inert gas, not reacting with the molten metals. Its thermal conductivity is high. It is not easy to ionize, requiring higher voltage to start the arc. Due to higher ionization potential it produces hotter arc at higher voltage, provides wide deep bead; this is an advantage for aluminium, magnesium, and copper alloys. Other gases are often added. Blends of helium with addition of 5–10% of argon and 2–5% of carbon dioxide ("tri-mix") can be used for welding of stainless steel. Used also for aluminium and other non-ferrous metals, especially for thicker welds. In comparison with argon, helium provides more energy-rich but less stable arc. Helium and carbon dioxide were the first shielding gases used, since the beginning of World War 2. Helium is used as a shield gas in laser welding for carbon dioxide lasers.[6] Helium is more expensive than argon and requires higher flow rates, so despite its advantages it may not be a cost-effective choice for higher-volume production.[7] Pure helium is not used for steel, as it then provides erratic arc and encourages spatter.
Oxygen is used in small amounts as an addition to other gases; typically as 2–5% addition to argon. It enhances arc stability and reduces the surface tension of the molten metal, increasing wetting of the solid metal. It is used for spray transfer welding of mild carbon steels, low alloy and stainless steels. Its presence increases the amount of slag. Argon-oxygen (Ar-O2) blends are often being replaced with argon-carbon dioxide ones. Argon-carbon dioxide-oxygen blends are also used. Oxygen causes oxidation of the weld,so it is not suitable for welding aluminium, magnesium, copper, and some exotic metals. Increased oxygen makes the shielding gas oxidize the electrode, which can lead to porosity in the deposit if the electrode does not contain sufficient deoxidizers. Excessive oxygen, especially when used in application for which it is not prescribed, can lead to brittleness in the heat affected zone. Argon-oxygen blends with 1–2% oxygen are used for austenitic stainless steel where argon-CO2 can not be used due to required low content of carbon in the weld; the weld has a tough oxide coating and may require cleaning.
Hydrogen is used for welding of nickel and some stainless steels, especially thicker pieces. It improves the molten metal fluidity, and enhances cleanness of the surface. It is added to argon in amounts typically under 10%. It can be added to argon-carbon dioxide blends to counteract the oxidizing effects of carbon dioxide. Its addition narrows the arc and increases the arc temperature, leading to better weld penetration. In higher concentrations (up to 25% hydrogen), it may be used for welding conductive materials such as copper. However, it should not be used on steel, aluminum or magnesium because it can cause porosity and hydrogen embrittlement; its application is usually limited only to some stainless steels.
Nitric oxide addition serves to reduce production of ozone. It can also stabilize the arc when welding aluminium and high-alloyed stainless steel.
Other gases can be used for special applications, pure or as blend additives; e.g. sulfur hexafluoride or dichlorodifluoromethane.[8]
Sulfur hexafluoride can be added to shield gas for aluminium welding to bind hydrogen in the weld area to reduce weld porosity.[9]
Dichlorodifluoromethane with argon can be used for protective atmosphere for melting of aluminium-lithium alloys.[10] It reduces the content of hydrogen in the aluminium weld, preventing the associated porosity.
Common mixes[edit]
Argon-carbon dioxide
C-50 (50% argon/50% CO2) is used for short arc welding of pipes,
C-40 (60% argon/40% CO2) is used for some flux-cored arc welding cases. Better weld penetration than C-25.
C-25 (75% argon/25% CO2) is commonly used by hobbyists and in small-scale production. Limited to short circuit and globular transfer welding. Common for short-circuit gas metal arc welding of low carbon steel.
C-20 (80% argon/20% CO2) is used for short-circuiting and spray transfer of carbon steel.
C-15 (85% argon/15% CO2) is common in production environment for carbon and low alloy steels. Has lower spatter and good weld penetration, suitable for thicker plates and steel significantly covered with mill scale. Suitable for short circuit, globular, pulse and spray transfer welding. Maximum productivity for thin metals in short-circuiting mode; has lower tendency to burn through than higher-CO2 mixes and has suitably high deposition rates.
C-10 (90% argon/10% CO2) is common in production environment. Has low spatter and good weld penetration, though lower than C-15; suitable for many steels. Same applications as 85/15 mix. Sufficient for ferritic stainless steels.
C-5 (95% argon/5% CO2) is used for pulse spray transfer and short-circuiting of low alloy steel. Has better tolerance for mill scale and better puddle control than argon-oxygen, though less than C-10. Less heat than C-10.[11] Sufficient for ferritic stainless steels. Similar performance to argon with 1% oxygen.
Argon-oxygen
O-5 (95% argon/5% oxygen) is the most common gas for general carbon steel welding. Higher oxygen content allows higher speed of welding. More than 5% oxygen makes the shielding gas oxidize the electrode, which can lead to porosity in the deposit if the electrode does not contain sufficient deoxidizers.
O-2 (98% argon/2% oxygen) is used for spray arc on stainless steel, carbon steels, and low alloy steels. Better wetting than O-1. Weld is darker and more oxidized than with O-1. The addition of 2% oxygen encourages spray transfer, which is critical for spray-arc and pulsed spray-arc GMAW.
O-1 (99% argon/1% oxygen) is used for stainless steels. Oxygen stabilizes the arc.
Argon-helium
A-25 (75% argon/25% helium) is used for nonferrous base when higher heat input and good weld appearance are needed.
A-50 (50% argon/50% helium) is used for nonferrous metals thinner than 0.75 inch for high-speed mechanized welding.
A-75 (25% argon/75% helium) is used for mechanized welding of thick aluminium. Reduces weld porosity in copper.[12]
Argon-hydrogen
H-2 (98% argon/2% hydrogen)
H-5 (95% argon/5% hydrogen)
H-10 (80% argon/20% hydrogen)
H-35 (65% argon/35% hydrogen)[13]
Others
Argon with 25–35% helium and 1–2% CO2 provides high productivity and good welds on austenitic stainless steels. Can be used for joining stainless steel to carbon steel.
Argon-CO2 with 1–2% hydrogen provides a reducing atmosphere that lowers amount of oxide on the weld surface, improves wetting and penetration. Good for austenitic stainless steels.
Argon with 2–5% nitrogen and 2–5% CO2 in short-circuiting yields good weld shape and color and increases welding speed. For spray and pulsed spray transfer it is nearly equivalent to other trimixes. When joining stainless to carbon steels in presence of nitrogen, care has to be taken to ensure the proper weld microstructure. Nitrogen increases arc stability and penetration and reduces distortion of the welded part. In duplex stainless steels assists in maintaining proper nitrogen content.
85–95% helium with 5–10% argon and 2–5% CO2 is an industry standard for short-circuit welding of carbon steel.
Argon – carbon dioxide – oxygen
Argon–helium–hydrogen
Argon – helium – hydrogen – carbon dioxide
Applications[edit]
The applications of shielding gases are limited primarily by the cost of the gas, the cost of the equipment, and by the location of the welding. Some shielding gases, like argon, are expensive, limiting its use. The equipment used for the delivery of the gas is also an added cost, and as a result, processes like shielded metal arc welding, which require less expensive equipment, might be preferred in certain situations. Finally, because atmospheric movements can cause the dispersion of the shielding gas around the weld, welding processes that require shielding gases are often only done indoors, where the environment is stable and atmospheric gases can be effectively prevented from entering the weld area.
The desirable rate of gas flow depends primarily on weld geometry, speed, current, the type of gas, and the metal transfer mode being utilized. Welding flat surfaces requires higher flow than welding grooved materials, since the gas is dispersed more quickly. Faster welding speeds, in general, mean that more gas needs to be supplied to provide adequate coverage. Additionally, higher current requires greater flow, and generally, more helium is required to provide adequate coverage than argon. Perhaps most importantly, the four primary variations of GMAW have differing shielding gas flow requirements—for the small weld pools of the short circuiting and pulsed spray modes, about 10 L/min (20 ft3/h) is generally suitable, while for globular transfer, around 15 L/min (30 ft3/h) is preferred. The spray transfer variation normally requires more because of its higher heat input and thus larger weld pool; along the lines of 20–25 L/min (40–50 ft3/h).[14]
See also[edit]
Forming gas
External links[edit]
Shielding Gas Handbook
References[edit]
Jump up ^ Lyttle, Kevin. (2005-01-11) Simplifying shielding gas selection. TheFabricator. Retrieved on 2010-02-08.
Jump up ^ The Evolution of Shielding Gas. Aws.org. Retrieved on 2010-02-08.
Jump up ^ Advanced welding supply gas type guide
Jump up ^ What You Should Know About Shielding Gas
Jump up ^ Choosing a Shielding Gas for Flux-Cored Welding
Jump up ^ Dawes, Christopher (1992), Laser welding: a practical guide, Woodhead Publishing, p. 89, ISBN 978-1-85573-034-2.
Jump up ^ Bernard – Great Welds Need The Right Gas: How Shielding Gas Can Make Or Break Your Weld Archived 2010-09-18 at the Wayback Machine.. Bernardwelds.com. Retrieved on 2010-02-08.
Jump up ^ Shielding gas for laser welding – Patent 3939323. Freepatentsonline.com. Retrieved on 2010-02-08.
Jump up ^ Method of welding material with reduced porosity – Patent Application 20070045238. Freepatentsonline.com (2005-08-29). Retrieved on 2010-02-08.
Jump up ^ Blanketing atmosphere for molten aluminum-lithium or pure lithium – Patent EP0268841. Freepatentsonline.com. Retrieved on 2010-02-08.
Jump up ^ Argon-Carbon Dioxide Mixtures – Praxair's StarGold and Mig Mix Gold Blends Archived 2010-01-13 at the Wayback Machine.. Praxair.com. Retrieved on 2010-02-08.
Jump up ^ Shielding Gases for Gas Metal Arc Welding (GMAW). Prest-o-sales.com. Retrieved on 2010-02-08.
Jump up ^ Shielding gas cross-reference chart
Jump up ^ Cary, Howard B.; Helzer, Scott C. (2005), Modern Welding Technology (6th ed.), Prentice Hall, pp. 123–125, ISBN 0-13-113029-3.
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Series and parallel circuits
From Wikipedia, the free encyclopedia
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A series circuit with a voltage source (such as a battery, or in this case a cell) and 3 resistors
Components of an electrical circuit or electronic circuit can be connected in many different ways. The two simplest of these are called series and parallel and occur frequently. Components connected in series are connected along a single path, so the same current flows through all of the components.[1][2] Components connected in parallel are connected along multiple paths, so the same voltage is applied to each component.[3]
A circuit composed solely of components connected in series is known as a series circuit; likewise, one connected completely in parallel is known as a parallel circuit.
In a series circuit, the current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component.[1] In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component.[1]
Consider a very simple circuit consisting of four light bulbs and one 6 V battery. If a wire joins the battery to one bulb, to the next bulb, to the next bulb, to the next bulb, then back to the battery, in one continuous loop, the bulbs are said to be in series. If each bulb is wired to the battery in a separate loop, the bulbs are said to be in parallel. If the four light bulbs are connected in series, there is same current through all of them, and the voltage drop is 1.5 V across each bulb, which may not be sufficient to make them glow. If the light bulbs are connected in parallel, the currents through the light bulbs combine to form the current in the battery, while the voltage drop is across each bulb and they all glow.
In a series circuit, every device must function for the circuit to be complete. One bulb burning out in a series circuit breaks the circuit. In parallel circuits, each light bulb has its own circuit, so all but one light could be burned out, and the last one will still function.
Contents
1 Series circuits
1.1 Current
1.2 Resistors
1.3 Inductors
1.4 Capacitors
1.5 Switches
1.6 Cells and batteries
1.7 Voltage
2 Parallel circuits
2.1 Voltage
2.2 Current
2.3 Resistors
2.4 Inductors
2.5 Capacitors
2.6 Switches
2.7 Cells and batteries
3 Combining conductances
4 Notation
5 Applications
6 See also
7 Notes
8 References
9 External links
Series circuits[edit]
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Series circuits are sometimes called current-coupled or daisy chain-coupled. The current in a series circuit goes through every component in the circuit. Therefore, all of the components in a series connection carry the same current.
A series circuit's principle characteristic is that it has only one path in which its current can flow. Opening or breaking a series circuit at any point causes the entire circuit to "open" or stop operating. For example, if even one of the light bulbs in an older-style string of Christmas tree lights burns out or is removed, the entire string becomes inoperable until the bulb is replaced.
Current[edit]
I = I 1 = I 2 = I 3 = ⋯ = I n {\displaystyle I=I_{1}=I_{2}=I_{3}=\cdots =I_{n}}
In a series circuit, the current is the same for all of the elements.
Resistors[edit]
The total resistance of resistors in series is equal to the sum of their individual resistances:
R total = R 1 + R 2 + ⋯ + R n {\displaystyle R_{\text{total}}=R_{1}+R_{2}+\cdots +R_{n}}
Electrical conductance presents a reciprocal quantity to resistance. Total conductance of a series circuits of pure resistors, therefore, can be calculated from the following expression:
1 G t o t a l = 1 G 1 + 1 G 2 + ⋯ + 1 G n {\displaystyle {\frac {1}{G_{\mathrm {total} }}}={\frac {1}{G_{1}}}+{\frac {1}{G_{2}}}+\cdots +{\frac {1}{G_{n}}}} .
For a special case of two resistors in series, the total conductance is equal to:
G total = G 1 G 2 G 1 + G 2 . {\displaystyle G_{\text{total}}={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}
Inductors[edit]
Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances:
L t o t a l = L 1 + L 2 + ⋯ + L n {\displaystyle L_{\mathrm {total} }=L_{1}+L_{2}+\cdots +L_{n}}
However, in some situations it is difficult to prevent adjacent inductors from influencing each other, as the magnetic field of one device couples with the windings of its neighbours. This influence is defined by the mutual inductance M. For example, if two inductors are in series, there are two possible equivalent inductances depending on how the magnetic fields of both inductors influence each other.
When there are more than two inductors, the mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the mutual inductance of each given coil with itself, which we term self-inductance or simply inductance. For three coils, there are six mutual inductances M 12 {\displaystyle M_{12}} , M 13 {\displaystyle M_{13}} , M 23 {\displaystyle M_{23}} and M 21 {\displaystyle M_{21}} , M 31 {\displaystyle M_{31}} and M 32 {\displaystyle M_{32}} . There are also the three self-inductances of the three coils: M 11 {\displaystyle M_{11}} , M 22 {\displaystyle M_{22}} and M 33 {\displaystyle M_{33}} .
Therefore
L t o t a l = ( M 11 + M 22 + M 33 ) + ( M 12 + M 13 + M 23 ) + ( M 21 + M 31 + M 32 ) {\displaystyle L_{\mathrm {total} }=(M_{11}+M_{22}+M_{33})+(M_{12}+M_{13}+M_{23})+(M_{21}+M_{31}+M_{32})}
By reciprocity M i j {\displaystyle M_{ij}} = M j i {\displaystyle M_{ji}} so that the last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such a coil all turns are in series.
Capacitors[edit]
See also: Capacitor § Networks
Capacitors follow the same law using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:
1 C t o t a l = 1 C 1 + 1 C 2 + ⋯ + 1 C n {\displaystyle {\frac {1}{C_{\mathrm {total} }}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+\cdots +{\frac {1}{C_{n}}}} .
Switches[edit]
Two or more switches in series form a logical AND; the circuit only carries current if all switches are closed. See AND gate.
Cells and batteries[edit]
A battery is a collection of electrochemical cells. If the cells are connected in series, the voltage of the battery will be the sum of the cell voltages. For example, a 12 volt car battery contains six 2-volt cells connected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed the 24 volt system.
Voltage[edit]
In a series circuit the voltage is addition of all the voltage elements.
V = V 1 + V 2 + ⋯ + V n {\displaystyle V=V_{1}+V_{2}+\dots +V_{n}}
Parallel circuits[edit]
"In Parallel" redirects here. For the 2017 Dhani Harrison album, see In Parallel (album).
If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff’s current law.
Voltage[edit]
In a parallel circuit the voltage is the same for all elements.
V = V 1 = V 2 = … = V n {\displaystyle V=V_{1}=V_{2}=\ldots =V_{n}}
Current[edit]
The current in each individual resistor is found by Ohm's law. Factoring out the voltage gives
I t o t a l = V ( 1 R 1 + 1 R 2 + ⋯ + 1 R n ) {\displaystyle I_{\mathrm {total} }=V\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}\right)} .
Resistors[edit]
To find the total resistance of all components, add the reciprocals of the resistances R i {\displaystyle R_{i}} of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:
1 R t o t a l = 1 R 1 + 1 R 2 + ⋯ + 1 R n {\displaystyle {\frac {1}{R_{\mathrm {total} }}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}} .
For only two resistors, the unreciprocated expression is reasonably simple:
R t o t a l = R 1 R 2 R 1 + R 2 . {\displaystyle R_{\mathrm {total} }={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}.}
This sometimes goes by the mnemonic product over sum.
For N equal resistors in parallel, the reciprocal sum expression simplifies to:
1 R t o t a l = N 1 R {\displaystyle {\frac {1}{R_{\mathrm {total} }}}=N{\frac {1}{R}}} .
and therefore to:
R t o t a l = R N {\displaystyle R_{\mathrm {total} }={\frac {R}{N}}} .
To find the current in a component with resistance R i {\displaystyle R_{i}} , use Ohm's law again:
I i = V R i {\displaystyle I_{i}={\frac {V}{R_{i}}}\,} .
The components divide the current according to their reciprocal resistances, so, in the case of two resistors,
I 1 I 2 = R 2 R 1 {\displaystyle {\frac {I_{1}}{I_{2}}}={\frac {R_{2}}{R_{1}}}} .
An old term for devices connected in parallel is multiple, such as a multiple connection for arc lamps.
Since electrical conductance G {\displaystyle G} is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors reads:
G t o t a l = G 1 + G 2 + ⋯ + G n {\displaystyle G_{\mathrm {total} }=G_{1}+G_{2}+\cdots +G_{n}} .
The relations for total conductance and resistance stand in a complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of conductances, and vice versa.
Inductors[edit]
Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
1 L t o t a l = 1 L 1 + 1 L 2 + ⋯ + 1 L n {\displaystyle {\frac {1}{L_{\mathrm {total} }}}={\frac {1}{L_{1}}}+{\frac {1}{L_{2}}}+\cdots +{\frac {1}{L_{n}}}} .
If the inductors are situated in each other's magnetic fields, this approach is invalid due to mutual inductance. If the mutual inductance between two coils in parallel is M, the equivalent inductor is:
1 L t o t a l = L 1 + L 2 − 2 M L 1 L 2 − M 2 {\displaystyle {\frac {1}{L_{\mathrm {total} }}}={\frac {L_{1}+L_{2}-2M}{L_{1}L_{2}-M^{2}}}}
If L 1 = L 2 {\displaystyle L_{1}=L_{2}}
L total = L + M 2 {\displaystyle L_{\text{total}}={\frac {L+M}{2}}}
The sign of M {\displaystyle M} depends on how the magnetic fields influence each other. For two equal tightly coupled coils the total inductance is close to that of each single coil. If the polarity of one coil is reversed so that M is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. It is assumed in the "tightly coupled" case M is very nearly equal to L. However, if the inductances are not equal and the coils are tightly coupled there can be near short circuit conditions and high circulating currents for both positive and negative values of M, which can cause problems.
More than three inductors becomes more complex and the mutual inductance of each inductor on each other inductor and their influence on each other must be considered. For three coils, there are three mutual inductances M 12 {\displaystyle M_{12}} , M 13 {\displaystyle M_{13}} and M 23 {\displaystyle M_{23}} . This is best handled by matrix methods and summing the terms of the inverse of the L {\displaystyle L} matrix (3 by 3 in this case).
The pertinent equations are of the form: v i = ∑ j L i , j d i j d t {\displaystyle v_{i}=\sum _{j}L_{i,j}{\frac {di_{j}}{dt}}}
Capacitors[edit]
The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:
C t o t a l = C 1 + C 2 + ⋯ + C n {\displaystyle C_{\mathrm {total} }=C_{1}+C_{2}+\cdots +C_{n}} .
The working voltage of a parallel combination of capacitors is always limited by the smallest working voltage of an individual capacitor.
Switches[edit]
Two or more switches in parallel form a logical OR; the circuit carries current if at least one switch is closed. See OR gate.
Cells and batteries[edit]
If the cells of a battery are connected in parallel, the battery voltage will be the same as the cell voltage, but the current supplied by each cell will be a fraction of the total current. For example, if a battery comprises four identical cells connected in parallel and delivers a current of 1 ampere, the current supplied by each cell will be 0.25 ampere. Parallel-connected batteries were widely used to power the valve filaments in portable radios, but they are now rare. Some solar electric systems have batteries in parallel to increase the storage capacity; a close approximation of total amp-hours is the sum of all amp-hours of in-parallel batteries.
Combining conductances[edit]
From Kirchhoff's circuit laws we can deduce the rules for combining conductances. For two conductances G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} in parallel, the voltage across them is the same and from Kirchhoff's current law (KCL) the total current is
I eq = I 1 + I 2 . {\displaystyle I_{\text{eq}}=I_{1}+I_{2}.\ \,}
Substituting Ohm's law for conductances gives
G eq V = G 1 V + G 2 V {\displaystyle G_{\text{eq}}V=G_{1}V+G_{2}V\ \,}
and the equivalent conductance will be,
G eq = G 1 + G 2 . {\displaystyle G_{\text{eq}}=G_{1}+G_{2}.\ \,}
For two conductances G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} in series the current through them will be the same and Kirchhoff's Voltage Law tells us that the voltage across them is the sum of the voltages across each conductance, that is,
V eq = V 1 + V 2 . {\displaystyle V_{\text{eq}}=V_{1}+V_{2}.\ \,}
Substituting Ohm's law for conductance then gives,
I G eq = I G 1 + I G 2 {\displaystyle {\frac {I}{G_{\text{eq}}}}={\frac {I}{G_{1}}}+{\frac {I}{G_{2}}}}
which in turn gives the formula for the equivalent conductance,
1 G eq = 1 G 1 + 1 G 2 . {\displaystyle {\frac {1}{G_{\text{eq}}}}={\frac {1}{G_{1}}}+{\frac {1}{G_{2}}}.}
This equation can be rearranged slightly, though this is a special case that will only rearrange like this for two components.
G eq = G 1 G 2 G 1 + G 2 . {\displaystyle G_{\text{eq}}={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}
Notation[edit]
The value of two components in parallel is often represented in equations by two vertical lines, ∥, borrowing the parallel lines notation from geometry.[4][5]
R e q ≡ R 1 ‖ R 2 ≡ ( R 1 − 1 + R 2 − 1 ) − 1 ≡ R 1 R 2 R 1 + R 2 {\displaystyle R_{\mathrm {eq} }\equiv R_{1}\|R_{2}\equiv \left(R_{1}^{-1}+R_{2}^{-1}\right)^{-1}\equiv {\frac {R_{1}R_{2}}{R_{1}+R_{2}}}}
This simplifies expressions that would otherwise become complicated by expansion of the terms. For instance:
R 1 ‖ R 2 ‖ R 3 ≡ R 1 R 2 R 3 R 1 R 2 + R 1 R 3 + R 2 R 3 {\displaystyle R_{1}\|R_{2}\|R_{3}\equiv {\frac {R_{1}R_{2}R_{3}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}}} .
Applications[edit]
A common application of series circuit in consumer electronics is in batteries, where several cells connected in series are used to obtain a convenient operating voltage. Two disposable zinc cells in series might power a flashlight or remote control at 3 volts; the battery pack for a hand-held power tool might contain a dozen lithium-ion cells wired in series to provide 48 volts.
Series circuits were formerly used for lighting in electric multiple unit trains. For example, if the supply voltage was 600 volts there might be eight 70-volt bulbs in series (total 560 volts) plus a resistor to drop the remaining 40 volts. Series circuits for train lighting were superseded, first by motor-generators, then by solid state devices.
Series resistance can also be applied to the arrangement of blood vessels within a given organ. Each organ is supplied by a large artery, smaller arteries, arterioles, capillaries, and veins arranged in series. The total resistance is the sum of the individual resistances, as expressed by the following equation: Rtotal = Rartery + Rarterioles + Rcapillaries. The largest proportion of resistance in this series is contributed by the arterioles.[6]
Parallel resistance is illustrated by the circulatory system. Each organ is supplied by an artery that branches off the aorta. The total resistance of this parallel arrangement is expressed by the following equation: 1/Rtotal = 1/Ra + 1/Rb + ... 1/Rn. Ra, Rb, and Rn are the resistances of the renal, hepatic, and other arteries respectively. The total resistance is less than the resistance of any of the individual arteries.[6]
See also[edit]
Network analysis (electrical circuits)
Wheatstone bridge
Y-Δ transform
Voltage divider
Current divider
Combining impedances
Equivalent impedance transforms
Resistance distance
Series-parallel partial order
Notes[edit]
^ Jump up to: a b c Resnick et al. (1966), Chapter 32, Example 1.
Jump up ^ Smith, R.J. (1966), page 21
Jump up ^ Resnick et al. (1966), Chapter 32, Example 4.
Jump up ^ http://www.en-genius.net/includes/files/avt_120406.pdf
Jump up ^ http://tex.stackexchange.com/questions/37912/how-to-draw-the-parallel-circuits-sign
^ Jump up to: a b Board Review Series: Physiology by Linda S. Costanzo pg. 74
References[edit]
Resnick, Robert and Halliday, David (1966), Physics, Vol I and II, Combined edition, Wiley International Edition, Library of Congress Catalog Card No. 66-11527
Smith, R.J. (1966), Circuits, Devices and Systems, Wiley International Edition, New York. Library of Congress Catalog Card No. 66-17612
Williams, Tim, The Circuit Designer's Companion, Butterworth-Heinemann, 2005 ISBN 0-7506-6370-7.
External links[edit]
Series circuit, Parallel circuit
Series and Parallel Circuits chapter from Lessons In Electric Circuits Vol 1 DC free ebook and Lessons In Electric Circuits series.
Series-Parallel Combination Circuits chapter from Lessons In Electric Circuits Vol 1 DC free ebook and Lessons In Electric Circuits series.
Sameen Ahmed Khan, How many equivalent resistances?, Resonance Journal of Science Education, Vol. 17, No. 5, 468-475 (May 2012).
Resistor combinations: How many values using 1K ohm resistors? - EDN magazine
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List of Liverpool F.C. records and statistics
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article is about all-time records. For a season-by-season statistical breakdown, see List of Liverpool F.C. seasons.
Steven Gerrard, Liverpool's record goalscorer in Europe
Liverpool Football Club are an English professional association football club based in Liverpool, Merseyside, who currently play in the Premier League. They have played at their current home ground, Anfield, since their foundation in 1892. Liverpool joined the Football League in 1894, and were founding members of the Premier League in 1992.
This list encompasses the major honours won by Liverpool, records set by the club, their managers and their players. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Liverpool players on the international stage, and the highest transfer fees paid and received by the club. Attendance records at Anfield are also included in the list.
The club have won 18 top-flight titles, and also hold the record for the most European Cup victories by an English team, winning the competition five times. The club's record appearance maker is Ian Callaghan, who made 857 appearances between 1958 and 1978. Ian Rush is the club's record goalscorer, scoring 346 goals in total.
Contents
[hide]
1 Honours
2 Player records
2.1 Appearances
2.2 Most appearances
2.3 Goalscorers
2.4 Top goalscorers
2.5 International
2.5.1 World Cup
3 Transfers
3.1 Record transfer fees paid
3.2 Record transfer fees received
4 Managerial records
5 Club records
5.1 Matches
5.1.1 Firsts
5.1.2 Wins
5.1.3 Defeats
5.2 Goals
5.3 Points
5.4 Attendances
6 European statistics
7 Footnotes
8 References
All statistics are correct as of 24 May 2015
Honours[edit]
Liverpool have won honours both domestically and in European cup competitions.[1] They have won the English League Championship 18 times and the League Cup a record eight times. In their first season, 1892–93, they won the Lancashire League title and the Liverpool District Cup,[2] and their most recent success came in 2012,[3] when they won the League Cup for the eighth time.[4]
Liverpool F.C. honours
Honour
No.
Years
Football League First Division
18 1900–01, 1905–06, 1921–22, 1922–23, 1946–47, 1963–64, 1965–66, 1972–73, 1975–76, 1976–77, 1978–79, 1979–80, 1981–82, 1982–83, 1983–84, 1985–86, 1987–88, 1989–90
Football League Second Division
4 1893–94, 1895–96, 1904–05, 1961–62
Lancashire League
1 1892–93
FA Cup
7 1965, 1974, 1986, 1989, 1992, 2001, 2006
League Cup
8 1981, 1982, 1983, 1984, 1995, 2001, 2003, 2012
FA Community/Charity Shield
15 1964*, 1965*, 1966, 1974, 1976, 1977*, 1979, 1980, 1982, 1986*, 1988, 1989, 1990*, 2001, 2006 (* shared)
Sheriff of London Charity Shield
1 1906
Football League Super Cup
1 1985-86
European Cup/UEFA Champions League
5 1977, 1978, 1981, 1984, 2005
UEFA Cup
3 1973, 1976, 2001
UEFA Super Cup
3 1977, 2001, 2005
Player records[edit]
Appearances[edit]
Most appearances in all competitions: Ian Callaghan, 857.[5]
Most league appearances: Ian Callaghan, 640.[5]
Most FA Cup appearances: Ian Callaghan, 79.[5]
Most League Cup appearances: Ian Rush, 78.[5]
Most Continental appearances: Jamie Carragher, 150.[5][6]
Youngest first-team player: Jerome Sinclair, 16 years and 6 days (against West Bromwich Albion, 26 September 2012).[5]
Oldest first-team player: Ned Doig, 41 years and 165 days (against Newcastle United, 11 April 1908).[5]
Oldest debutant: Ned Doig, 37 years and 307 days (against Burton United, 1 September 1904).[5]
Most consecutive appearances: Phil Neal, 417 (from 23 October 1976 to 24 September 1983).[5]
Most seasons playing every minute of every league and cup game: Phil Neal, 9 (from 1976–77 to 1983–84).[5]
Longest-serving player: Elisha Scott, 21 years and 52 days (from 1913 to 1934).[5]
Most appearances[edit]
Competitive, professional matches only, appearances as substitute in brackets.[7][8]
Players with most appearances for Liverpool F.C.
No.
Name
Years
League[C]
FA Cup
League Cup
Other[D]
Total
1
Callaghan, IanIan Callaghan
1960–1978 640 !640 (4) 79 !79 (2) 42 !42 (7) 96 !96 (1) 857 !857 (14)
2
Carragher, JamieJamie Carragher
1996–2013 508 !508 (24) 40 !40 (1) 35 !35 (7) 152 !152 (3) 737 !737 (35)
3
Gerrard, StevenSteven Gerrard
1998–2015 504 !504 (39) 42 !42 (5) 30 !30 (5) 134 !134 (14) 710 !710 (63)
4
Clemence, RayRay Clemence
1967–1981 470 !470 (0) 54 !54 (0) 55 !55 (0) 86 !86 (0) 665 !665 (0)
Hughes, EmlynEmlyn Hughes
1967–1979 474 !474 (0) 62 !62 (0) 46 !46 (0) 83 !83 (0) 665 !665 (0)
6
Rush, IanIan Rush
1980–1987
1988–1996 469 !469 (22) 61 !61 (5) 78 !78 (0) 45 !45 (3) 660 !660 (30)
7
Neal, PhilPhil Neal
1974–1985 455 !455 (2) 45 !45 (0) 66 !66 (0) 81 !81 (0) 650 !650 (2)
8
Smith, TommyTommy Smith
1962–1978 467 !467 (0) 52 !52 (0) 30 !30 (0) 89 !89 (1) 638 !638 (1)
9
Grobbelaar, BruceBruce Grobbelaar
1980–1994 440 !440 (0) 62 !62 (0) 70 !70 (0) 46 !46 (0) 628 !628 (0)
10
Hansen, AlanAlan Hansen
1977–1991 434 !434 (0) 58 !58 (1) 68 !68 (0) 53 !53 (1) 620 !620 (2)
Goalscorers[edit]
Robbie Fowler, who scored the fastest hat-trick in Liverpool history
Most goals in all competitions: Ian Rush, 346.[9]
Most league goals: Roger Hunt, 245.[9]
Most FA Cup goals: Ian Rush, 39.[9]
Most League Cup goals: Ian Rush, 48.[9]
Most Continental goals: Steven Gerrard, 41.[9]
Most goals in a season: Ian Rush, 47 (during the 1983–84 season).[10]
Most goals in a debut season: Mohamed Salah, 44 (during the 2017–18 season).[11]
Most league goals in a season: Roger Hunt, 41 (during the 1961–62 season).[12]
Most goals in a season by a Liverpool player in the Premier League era: Mohamed Salah, 44 (during the 2017–18 season).[13]
Most top-flight league goals in a season: 32 goals, Mohamed Salah, 2017–18 and Ian Rush, 1983–84.
Most continental goals in a season: Mohamed Salah and Roberto Firmino, 11 (during the 2017–18 season).[14]
Most hat-tricks in a season: Roger Hunt, 5 (during the 1961–62 season).[9]
Most games scored in a single campaign: Mohamed Salah, 34 (during the 2017–18 Premier League season).
Most goals in a season by a Liverpool player in history of Premier League: Mohamed Salah, 32 (during the 2017–18 season).[15]
Most hat-tricks: Gordon Hodgson, 17.[9]
Fastest hat-trick: Robbie Fowler, 4 minutes, 33 seconds, (against Arsenal, 28 August 1994).[9]
Highest-scoring substitute: David Fairclough, 18.[9]
Most penalties scored: Steven Gerrard, 47.[9]
Most games without scoring for an outfield player: Ephraim Longworth, 371.[9]
Youngest goalscorer: Ben Woodburn, 17 years, 45 days (against Leeds United, 29 November 2016).[9][16][17]
Oldest goalscorer: Billy Liddell, 38 years, 55 days (against Stoke City, 5 March 1960).[9]
Top goalscorers[edit]
Competitive, professional matches only. Matches played (including as substitute) appear in brackets.[18][19]
Top goalscorers for Liverpool F.C.
No.
Name
Years
League[C]
FA Cup
League Cup
Other[D]
Total
1
Rush, IanIan Rush
1980–1987
1988–1996 229 !229 (469) 39 !39 (61) 48 !48 (78) 23 !23 (45) 346 !346 (660)
2
Hunt, RogerRoger Hunt
1958–1969 245 !245 (404) 18 !18 (44) 05 !5 (10) 18 !18 (34) 286 !286 (492)
3
Hodgson, GordonGordon Hodgson
1925–1936 233 !233 (358) 08 !8 (19) 00 !0 (0) 00 !0 (0) 241 !241 (377)
4
Liddell, BillyBilly Liddell
1938–1961 215 !215 (492) 13 !13 (42) 00 !0 (0) 00 !0 (0) 228 !228 (534)
5
Gerrard, StevenSteven Gerrard
1998–2015 120 (503) 15 !15 (40) 9 !9 (28) 42 !42(132) 186 !186 (710)
6
Fowler, RobbieRobbie Fowler
1993–2001
2006–2007 128 !128 (266) 12 !12 (24) 29 !29 (35) 14 !14 (44) 183 !183 (369)
7
Dalglish, KennyKenny Dalglish
1977–1990 118 !118 (355) 13 !13 (37) 27 !27 (59) 12 !12 (58) 172 !172 (515)
8
Owen, MichaelMichael Owen
1996–2004 118 !118 (216) 08 !8 (15) 09 !9 (14) 23 !23 (52) 158 !158 (297)
9
Chambers, HarryHarry Chambers
1915–1928 135 !135 (315) 16 !16 (28) 00 !0 (0) 00 !0 (1) 151 !151 (339)
10
Parkinson, JackJack Parkinson
1903–1914 125 !125 (200) 05 !5 (19) 00 !0 (0) 00 !0 (1) 130 !130 (220)
International[edit]
First capped player: Frank Becton, for England on 29 March 1897.[20]
Most international caps while a Liverpool player: Steven Gerrard, 114 for England.[21]
Most international goals while a Liverpool player:[21]
Michael Owen, 26 for England.
Ian Rush, 26 for Wales.
World Cup[edit]
First Liverpool player to appear at a World Cup: Laurie Hughes for England, at 1950 FIFA World Cup.[22]
Most World Cup appearances while a Liverpool player: Steven Gerrard, 12 for England in 2006, 2010 and 2014.[21]
Most World Cup goals while a Liverpool player: Michael Owen, 4 for England in 1998 and 2002.[21]
First World Cup winners: Roger Hunt, Ian Callaghan and Gerry Byrne, in 1966 with England.[21]
First non-British player to appear in a World Cup final: Dietmar Hamann, Germany, in 2002.[21]
First non-British World Cup winners: Fernando Torres and Pepe Reina, Spain in 2010.[22]
Transfers[edit]
For consistency, fees in the record transfer tables below are all sourced from BBC Sport's contemporary reports of each transfer.
Record transfer fees paid[edit]
Record transfer fees paid by Liverpool F.C.
For
Fee
Paid to
Date
Ref
van Dijk, VirgilVirgil van Dijk
£75m Southampton F.C 000000002018-01-01-00001 January 2018 [23]
Keïta, NabyNaby Keïta
£48m RB Leipzig 000000002018-07-01-00001 July 2018 [24]
Fabinho
£39m AS Monaco 000000002018-05-28-000028 May 2018 [25]
Salah, MohamedMohamed Salah
£36.9m A.S. Roma 000000002017-06-23-000023 June 2017 [26]
Carroll, AndyAndy Carroll
£35m Newcastle United 000000002011-01-31-000031 January 2011 [27]
Oxlade-Chamberlain, Alex Alex Oxlade-Chamberlain
£35m Arsenal F.C. 000000002017-08-31-000031 August 2017 [28]
Record transfer fees received[edit]
Record transfer fees received by Liverpool F.C.
For
Fee
Received from
Date
Ref
Coutinho, PhilippePhilippe Coutinho
£142m Barcelona 000000002018-01-06-00006 January 2018 [29]
Suárez, LuisLuis Suárez
£75m Barcelona 000000002014-07-11-000011 July 2014 [30]
Torres, FernandoFernando Torres
£50m Chelsea 000000002011-01-31-000031 January 2011 [31]
Sterling, RaheemRaheem Sterling
£49m Manchester City 000000002015-07-14-000014 July 2015 [32]
Alonso, XabiXabi Alonso
£30m Real Madrid 000000002009-08-05-00005 August 2009 [33]
Benteke, ChristianChristian Benteke
£27m Crystal Palace 000000002016-08-20-000020 August 2016 [34]
Managerial records[edit]
Tom Watson, Liverpool's longest-serving manager
First managers: William Edward Barclay and John McKenna, from 15 February 1892 to 16 August 1896.[35]
Longest-serving manager by time: Tom Watson, from 17 August 1896 to 6 May 1915 (18 years, 262 days).[5]
Longest-serving manager by matches: Bill Shankly managed the club for 783 matches over a period of 14 years and seven months, from December 1959 to July 1974.[5]
Club records[edit]
Matches[edit]
Firsts[edit]
First match: Liverpool 7–1 Rotherham Town, a friendly match, 1 September 1892.[36]
First Lancashire League match: Liverpool 8–0 Higher Walton, 3 September 1892.[36]
First Football League match: Liverpool 2–0 Middlesbrough Ironopolis, Second Division, 2 September 1893.[36]
First FA Cup match: Liverpool 4–0 Nantwich Town, first qualifying round, 15 October 1892.[36]
First League Cup match: Liverpool 1–1 Luton Town, second round, 19 October 1960.[36]
First European match: Liverpool 5–0 KR Reykjavik, European Cup, first round, 17 August 1964.[36]
Wins[edit]
Record win: 11–0 against Strømsgodset in the UEFA Cup Winners' Cup, 17 September 1974.[36]
Record league win: 10–1 against Rotherham Town in Second Division, 18 February 1896.[36]
Record FA Cup win: 9–0 against Newtown in second qualifying round, 29 October 1892.[36]
Record League Cup win: 10–0 against Fulham in second round, first-leg, 23 September 1986.[36]
Most league wins in a season: 30 wins from 42 games (during the 1978–79 season).[36]
Fewest league wins in a season: 7 wins from 30 games (during the 1894–95 season).[36]
Defeats[edit]
Record defeat: 1–9 against Birmingham City FC in Second Division, 11 December 1954.[36]
Record defeat at Anfield: 0–6 against Sunderland in First Division, 19 April 1930.[36]
Record-scoring defeat: 2–9 against Newcastle United in First Division, 1 January 1934.[36]
Record FA Cup defeat: 0–5 against Bolton Wanderers in fourth round, first-leg, 26 January 1946.[36]
Record League Cup defeat: 3–6 against Arsenal in fifth round, 9 January 2007.[36]
Most league defeats in a season: 23 defeats from 42 games (during the 1953–54 season).[36]
Fewest defeats in a season: Unbeaten during the 28-game 1893–94 season.[36]
Goals[edit]
Most league goals scored in a season: 106 in 30 games (during the 1895–96 season, Second Division).[9]
Most Top flight goals scored in a season: 101 in 38 games (during the 2013–14 season, Premier League).[9]
Fewest league goals scored in a season: 42 in 34 and 42 games (during the 1901–02 and 1970–71 seasons, First Division).[9]
Most league goals conceded in a season: 97 in 42 games (during the 1953–54 season, First Division).[9]
Fewest league goals conceded in a season: 16 in 42 games (during the 1978–79 season, First Division).[9]
Points[edit]
Most points in a season:
Two points for a win: 68 (in 42 games in 1978–79, First Division).[37]
Three points for a win: 90 (in 40 games in 1987–88, First Division).[37]
Fewest points in a season:
Two points for a win: 22 (in 30 games in 1894–95, First Division).[37]
Three points for a win: 52 (in 38 games in 2011–12, Premier League).[38]
Attendances[edit]
Highest league attendance: 58,757 (against Chelsea, First Division in the 1949–50 season).[39]
Highest League Cup attendance: 50,880 (against Nottingham Forest, in the 1979–80 season).[39]
Highest European attendance: 55,104 (against Barcelona, in the 1975–76 season).[39]
Record lowest attendance: 1,000 (against Loughborough, Second Division in the 1895–96 season).[39][F]
Lowest FA Cup attendance: 4,000 (against Newtown, in the 1892–93 season).[39]
Lowest League Cup attendance: 9,902 (against Brentford in the 1983–84 season).[39]
Lowest European attendance: 12,021 (against Dundalk in the 1982–83 season).[39]
Liverpool recorded a 95,446 attendance against Melbourne Victory in a pre-season friendly in July 2013 at the Melbourne Cricket Ground, Australia.[40]
European statistics[edit]
Main article: Liverpool F.C. in European football
Footnotes[edit]
A. ^ Between 1949 and 1993 the Community Shield was usually shared if the game was drawn.
B. ^ Ever-present refers to the player playing every minute of every match in the league and cup competitions.
C. a b Includes the Football League and the Premier League.
D. a b The "Other" column includes goals and appearances (including those as a substitute) in UEFA Champions League, UEFA Cup, UEFA Cup Winners Cup, UEFA Super Cup, Charity Shield and Intercontinental Cup matches.
E. ^ Attendance against Wolves also represents the record highest FA Cup attendance.
F. ^ Attendance against Loughborough also represents the record lowest league attendance.
References[edit]
General
"Stats". LFC history. Archived from the original on 24 February 2008. Retrieved 14 February 2008.
"Records". Liverpool F.C. Archived from the original on 12 February 2008. Retrieved 17 February 2008.
Specific
Jump up ^ "Liverpool FC".
Jump up ^ "LFC Story". Liverpool F.C. Archived from the original on 15 February 2008. Retrieved 18 February 2008.
Jump up ^ "The History of Liverpool Football Trophies". afordawards.co.uk. 18 December 2013. Retrieved 2 June 2017.
Jump up ^ "Honours". Liverpool F.C. Retrieved 27 August 2012.
^ Jump up to: a b c d e f g h i j k l m "Appearances". Liverpool F.C. Archived from the original on 13 August 2012. Retrieved 27 August 2012.
Jump up ^ "Total games played per season by Jamie Carragher". LFC history. Archived from the original on 6 August 2007. Retrieved 15 February 2008.
Jump up ^ Pead 1986, p. 416
Jump up ^ "Most Appearances". LFC history. Archived from the original on 16 June 2010. Retrieved 22 February 2008.
^ Jump up to: a b c d e f g h i j k l m n o p q r "Goals". Liverpool F.C. Archived from the original on 13 August 2012. Retrieved 24 February 2016.
Jump up ^ Rollin 2006, pp. 232–233
Jump up ^ "Most goals in a debut season". lfchistory.net. Retrieved 2018-04-30.
Jump up ^ "Season". Liverpool F.C. Archived from the original on 13 August 2012. Retrieved 25 March 2014.
Jump up ^ "Mohamed Salah breaking records with Liverpool scoring exploits". skysports.com. Retrieved 2018-03-31.
Jump up ^ "Salah, Firmino make history with goals vs. City". ESPN.com. Retrieved 2018-04-11.
Jump up ^ "Mohamed Salah wins Golden Boot with new PL record". The Independent. 13 May 2018. Retrieved 13 May 2018.
Jump up ^ Price, Glenn (29 November 2016). "Liverpool forward Ben Woodburn becomes Liverpool's youngest scorer". espnfc.com.
Jump up ^ Carroll, James (29 November 2016). "Liverpool FC's youngest ever first-team goalscorers". Liverpool F.C. Retrieved 30 November 2016.
Jump up ^ Pead 1986, p. 415
Jump up ^ "Goalscorers". LFC history. Archived from the original on 24 February 2008. Retrieved 22 February 2008.
Jump up ^ Pead 1986, p. 396
^ Jump up to: a b c d e f "Internationals". Liverpool F.C. Archived from the original on 3 March 2016. Retrieved 24 February 2016.
^ Jump up to: a b "Liverpool & World Cup". LFC history. Archived from the original on 13 December 2007. Retrieved 25 December 2007.
Jump up ^ "Virgil van Dijk: Liverpool to sign Southampton defender for world record £75m". BBC Sport. 27 December 2017. Retrieved 27 December 2017.
Jump up ^ "Naby Keita: Liverpool agree club record deal for Leipzig midfielder for July 2018". BBC Sport. 29 August 2017. Retrieved 29 August 2017.
Jump up ^ "Fabinho:Liverpool agree £39m deal for Monaco midfielder". BBC Sport. 28 May 2018. Retrieved 28 May 2018.
Jump up ^ "Mohamed Salah: Liverpool sign Roma's former Chelsea winger for £36.9m". BBC Sport. 23 June 2017. Retrieved 23 June 2017.
Jump up ^ "Liverpool sign Andy Carroll from Newcastle". BBC Sport. 31 January 2011. Retrieved 31 January 2011.
Jump up ^ "Alex Oxlade-Chamberlain: Liverpool sign Arsenal midfielder for £35m". BBC Sport. 31 August 2017. Retrieved 31 August 2017.
Jump up ^ "Philippe Coutinho: Barcelona to sign Liverpool and Brazil midfielder in £142m deal". BBC Sport. 6 January 2018. Retrieved 10 January 2018.
Jump up ^ "Liverpool & Barcelona agree £75m deal for striker". BBC Sport. 11 July 2014. Retrieved 11 July 2014.
Jump up ^ "Torres makes record move from Liverpool to Chelsea". BBC Sport. 31 January 2011. Retrieved 31 January 2011.
Jump up ^ "Raheem Sterling: Man City sign Liverpool winger in £49m deal". BBC Sport. 14 July 2015. Retrieved 14 July 2015.
Jump up ^ "Alonso completes £30m Real move". BBC Sport. 5 August 2009. Retrieved 5 August 2009.
Jump up ^ "Christian Benteke: Crystal Palace sign striker from Liverpool for £27m". BBC Sport. 20 August 2016. Retrieved 20 August 2016.
Jump up ^ "John McKenna's managerial career". LFC history. Archived from the original on 15 December 2007. Retrieved 3 October 2007.
^ Jump up to: a b c d e f g h i j k l m n o p q r s "Matches". Liverpool F.C. Archived from the original on 12 September 2015. Retrieved 27 August 2012.
^ Jump up to: a b c Pead 1986, p. 414
Jump up ^ "Kenny Dalglish fact file". ITV Sport. 17 May 2012. Archived from the original on 27 January 2013. Retrieved 19 May 2012.
^ Jump up to: a b c d e f g "Attendances". Liverpool F.C. Archived from the original on 12 September 2015. Retrieved 27 August 2012.
Jump up ^ "Liverpool FC stamps Melbourne as world sports leader". 25 July 2013. Retrieved 21 February 2014.
Bibliography
Pead, Brian (1986). Liverpool A Complete Record. Breedon Books. p. 416. ISBN 0-907969-15-1.
Ponting, Ivan. Liverpool in Europe. Guinness. p. 22. ISBN 0-85112-569-7.
Rollin, Jack and Glenda (2006). Sky Sports Football Yearbook 2006-2007. Headline. pp. 232–233. ISBN 0-7553-1526-X.
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