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Question

# The e.m.f of the driver cell of a potentiometer is 2 V and its internal resistance is negligible. The length of the potentiometer wire is 100 cm and resistance is 5 Ω. How much resistance is to be connected in series with the potentiometer wire to have a potential gradient of 0.05 mV/cm ?

A
1990 Ω
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B
2000 Ω
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C
1995 Ω
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D
None of these
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Solution

## The correct option is C 1995 ΩGiven, E=2 V; R=5 Ω; l=100 cm K=0.05 mV/cm=0.05×10−3 V/cm If R′ is the external resistance connected with the battery of zero internal resistance and a potentiometer wire having resistance R then, i=ER+R′=KlR After putting the value of given data 25+R′=(0.05×10−3)×1005 10000=25+5R′⇒5R′=9975 ∴R=1995 Ω Hence, option (c) is correct.

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