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Question

A potentiometer wire has length 4 m and resistance 8Ω. The resistance that must be connected in series with the wire and an accumulator of e.m.f 2V, so as to get a potential gradient 1 mV per cm on the wire is

A
44Ω
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B
48Ω
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C
32Ω
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D
40Ω
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Solution

The correct option is C 32Ωthe total resistance after adding resistance R in series with potentiometer wire =8Ω+RΩthe current in the circuit will be i=V/Req=2VR+8the potential drop across potentiometer wire will be iRpotentiometer=2VR+8×8the potential gradient along length 4 m is given as =Vpotetiometer=2VR+8×84 the gradient is given as 1mV/cm=.1V/m2VR+8×84=.1R=32Ω

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