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Q.

In an experiment to measure the internal resistance of a cell by potentiometer it is found that the balance point is at a length of 2 m when the cell is shunted by a 5 Ω  resistance and is at a length 3 m  when the cell is shunted by a 10 Ω  resistance. The internal resistance of the cell is

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a

1.5  Ω

b

10  Ω

c

15  Ω

d

1  Ω

answer is B.

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Detailed Solution

Let say length without external resistance is l r=  ll'−1R ∴  r = l2−1 × 5  →(1) ∴  r = l3−1 × 10  →(2) From eq. (1) and (2) ∴  r = l2−1 × 5 =  l3−1 × 10 ⇒l2 −1  = 2l3−2 ⇒ l = 6 m hence , r = l2 −1×5=62 −1×5 =10 Ω
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In an experiment to measure the internal resistance of a cell by potentiometer it is found that the balance point is at a length of 2 m when the cell is shunted by a 5 Ω  resistance and is at a length 3 m  when the cell is shunted by a 10 Ω  resistance. The internal resistance of the cell is