Current Electricity 4 Question 4

4. In a meter bridge, the wire of length 1m has a non-uniform cross-section such that the variation dRdl of its resistance R with length l is dRdl1l.

Two equal resistance are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?

(2019 Main, 12 Jan I)

(a) 0.3m

(b) 0.25m

(c) 0.2m

(d) 0.35m

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Solution:

  1. As, galvanometer shows zero deflection.

This means, the meter bridge is balanced.

RRAP=RRPBRAP=RPB

Now, for meter bridge wire

dRdl=kl

where, ’ k ’ is the constant of proportionality.

dR=kldl

Integrating both sides, we get

R=kldl So, RAP=0lkldl=k(2l)|0l=2kl and RPB=l1kldl=2k(l)|l1=2k(1l)=2k(1l)

Substituting values of RAP and RPB in eq. (i), we get

RAP=RPB2kl=2k(1l)l=12 or l=14=0.25m



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