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A number of indentical cells, n, each of...

A number of indentical cells, n, each of emf `epsilon`, internal resistance r, connected in series are charged by a d.c. source of emf `epsilon'` , using a resistor R.(i) Draw the circuit arrangemnet. (ii) Deduce the expression for (a) the charging current and (b) the potential difference across the combination of the cells

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(i) The circuit arrangment for charging the cells is shows in figure

(ii) Effective emf of the circuit = `epsilon' - n epsilon`
Total resistance `= R+ nr`
Charging current `I= ("effective emf")/("total resistnance") = (epsilon' - n epsilon)/( R +nr)`
(iii) Pot. diff. across each charging cell `= epsilon + Ir`
`epsilon + ((epsilon' -n epsilon)/(R + nr)) r = (epsilon R + epsilon' r)/(R + nr)`
Pot. diff. across the series combination of n cells
`V = n (epsilon + Ir) = n ((epsilon R + epsilon'r)/(R + nr))`
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