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Question

n identical cells, each of internal resistance (r) are first connected in parallel and then connected in series across a resistance (R). If the current through R is same in both the cases then:

A
R=r/2
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B
r=R/2
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C
R=r
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D
r=0
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Solution

The correct option is C R=r
If the emf of each cell be E, then for parallel connection, equivalent emf is

Eeq=E1r1+E2r2+....1r1+1r2+....=Er+Er+....1r+1r+.....=E

And equivalent internal resistance of the cells, req=rn

So net current in parallel connection is

Ip=Eeqreq+R=Ern+R

And for series connection of cells, eqv emf , Eeq=E1+E2+...=nE

and equivalent internal resistance for series, req=r1+r2+....=nr

So current ,Is=Eeqreq+R=nEnr+R

Now according to question, both the currents are equal.

So, Ip=Is reduces to Ern+R=nEnr+R which gives R=r

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