First slide

Electrical measuring instruments

Question

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

Easy

A

$1.5 Ω$
B

$10 Ω$
C

$15 Ω$
D

$1 Ω$

Solution

$L e t s a y l e n g t h w i t h o u t e x t e r n a l r e s i s \tan c e i s l r = (\frac{l}{l'} - 1) R ∴ r = (\frac{l}{2} - 1) \times 5 \to (1) ∴ r = (\frac{l}{3} - 1) \times 10 \to (2) F r o m e q . (1) a n d (2) ∴ r = (\frac{l}{2} - 1) \times 5 = (\frac{l}{3} - 1) \times 10 \Rightarrow \frac{l}{2} - 1 = \frac{2 l}{3} - 2 \Rightarrow l = 6 m h e n c e, r = (\frac{l}{2} - 1) \times 5 = (\frac{6}{2} - 1) \times 5 = 10 Ω$

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