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E.M.F. Internal Resistance


single cell


cells series

cells parallel



The Single Cell


E.M.F.(E) is the p.d. across a cell when it delivers no current.


It can also be thought of as the energy converted into electrical energy, when 1 Coulomb of charge passes through it.


The internal resistance(r) of a cell is a very small resistance. For a 'lead-acid' cell it is of the order of 0.01 Ω and for a 'dry' cell it is about 1 Ω.


This means that a lead-acid cell will deliver a higher current than a dry cell.


We can obtain important equations for E and r by considering a cell with a resistance in a circuit.



cell internal resistance



The total resistance Rtotal is the sum of the series resistor and the internal resistance of the cell.


internal resistance equation #2


by summing p.d. around the circuit ,


internal resistance equation #3


substituting for Rtotal


internal resistance equation #1


by Ohm's law, substituting IR = VR


internal resistance #4


Note, VR is called the terminal p.d. . That is the p.d. across the cell when it is delivering current.


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Measurement of E & r


measurement of EMF & internal resistance



After taking readings of terminal p.d. (VR) and current (I), a graph is drawn.



measurement of EMF 7 internal resistance



Information can be obtained from the graph by manipulating the equation obtained for E and r:


internal resisitance and EMF equation


EMF and internal resistance equation #1


transposing the I and r, turning the equation around,


measurement of EMF and internal resistance equation #2


comparing with the equation of a straight line,


y equals mx plus c


Therefore the gradient is '- r' and the intercept on the vertical axis is 'E' .


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Cells in Series


electric cells in series



cells in series equation #1




cells in series equation #2




cells in series equation #3

where r is the internal resistance of the combination



cells in series equation #4



So to sum up, two cells in series are equivalent to one cell with an EMF equal to the sum of the two cells.


The internal resistance of the combination is the sum of the internal resistances of the two cells.


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Cells in Parallel


The arrangement dealt with here is only for cells that are similar. For disimilar cells the relationship is complicated, but can be resolved using Kirchhoff's Laws.



cells in parallel



For similar cells the EMF's are equal and the internal resistances are also equal.


Therefore the combined EMF, E is given by,


cells in parallel equation #1


and the internal resistance of the combination is calculated from the two internal resistances in parallel:


cells in parallel equation #2




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