Current Electricity 4 Question 2

2. In the circuit shown, a four-wire potentiometer is made of a 400cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is r=0.01 Ω/cm. If an ideal voltmeter is connected as shown with jockey J at 50cm from end A, the expected reading of the voltmeter will be

(a) 0.20V

(b) 0.75V

(c) 0.25V

(d) 0.50V

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Solution:

  1. In given potentiometer, resistance per unit length is x=0.01Ωcm1.

Length of potentiometer wire is L=400cm

Net resistance of the wire AB is

RAB= resistance per unit length × length of AB

=0.01×400

RAB=4Ω

Net internal resistance of the cells connected in series,

r=0.5+0.5=1Ω

Current in given potentiometer circuit is

I= Net emf  Total resistance = Net emf r+R+RAB=31+1+4=0.5A

Reading of voltmeter when the jockey is at 50cm(l) from one end A,

V=IR=I(xl)=0.5×0.01×50=0.25V



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