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Question

A potentiometer has a uniform potential gradient across it. Two cells connected in series - (i) to support each other and (ii) to oppose each other are balanced over 6 m and 2 m respectively on the potentiometer wire. The emfs of the cells are in the ratio

A
1 : 4
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B
1 : 1
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C
3 : 1
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D
2 : 1
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Solution

The correct option is D 2 : 1
Let, the L lenght wire having resistance of R0,
then, the resistance of x wire =xR0L

Case-1: In support condition

E1+E2=6R0L ....(1)

Case 2: In oppose condition

E1E2=2R0L ....(2)

Eq.(1)Eq.(2)=E1+E2E1E2=31E1+E2=3(E1E2)

Hence, E1E2=21
E1:E2=2:1

hence, option (d) is correct.

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