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If n batches of m cells in series are connected in parallel with an external resistance R, then what is the expression for current I through R

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Circuit diagram

Each row of n cells connected in series  provides emf = nE . The equivalent resistance of each row is also nr. Hence for m rows (parallel connection) the net equivalent resistance becomes (nr)/m.

The emf across the external resistance R is nE.

Hence main current of the circuit

I=nE/(R+nr/m)

if r=0 then I =nE/R

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