First slide

Electrical measuring instruments

Question

In a meter bridge , the wire of length 1 m has a non-uniform cross-section such that, the variation $\frac{d R}{d l}$ of its resistance R with length $l$ is $\frac{d R}{d l} α \frac{1}{\sqrt{l}}$ , two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?

Moderate

A

0.25m
B

0.3m
C

0.35m
D

0.2m

Solution

$F o r t h e g i v e n w i r e; d R = \frac{C d l}{\sqrt{l}} w h e r e c = c o n s \tan t L e t r e s i s \tan c e o f p a r t A P a n d P B i s R_{1} a n d R_{2} r e s p . N o w, \int d R = C \int \frac{d l}{\sqrt{l}} R_{1} = C \int_{0}^{l} l^{- 1 / 2} d l = C .2. \sqrt{l} R_{2} = C \int_{l}^{1} l^{- 1 / 2} d l = 2 C . (1 - \sqrt{l}) P u t t i n g R_{1} = R_{2} C 2 \sqrt{l} = 2 C [1 - \sqrt{l}] \Rightarrow 2 \sqrt{l} = 1 \Rightarrow \sqrt{l} = 1 / 2 \Rightarrow l = 1 / 4 m = 0.25 m$

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