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Q.

The balancing lengths of potentiometer wire are l1 and l2 when two cells of emf E1 and E2 are connected in the secondary circuit in series first to help each other and next to oppose each other E1E2 is equal to E1>E2. 

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a

l1l2

b

l2l1

c

l1+l2l1−l2

d

l1−l2l1+l2

answer is C.

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Detailed Solution

Let potential gradient be k, 

For the supporting arrangement :

E1+E2=kl1

For the opposing arrangement :

E1-E2=kl2

From the above 2 equations :

E1 = k(l1+l2)

E2 = k(l1-l2)

∴E1E2=(l1+l2)(l1-l2)

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