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Question

# A cell of e.m.f E volt with no internal resistance is connected to a wire whose cross-section changes. The wire has three sections of equal length l. The middle section has a radius a, whereas the radius of the outer two sections is 2a. The ratio of the potential difference across section AB to the potential difference across section CA is

A
5
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B
4
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C
12
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D
14
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Solution

## The correct option is B 4Let ρ be the resistivity of the given wire. Resistance of bigger and smaller section will be RAB=ρlπa2; RCA=ρl4πa2 In series combination, current I is constant. ∴V∝R (∵V=IR) So, for the given section VABVCA=RABRCA ⇒VABVCA=ρlπa2ρl4πa2=41=4 Hence, option (b) is correct.

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