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Electrostatic Potential And Capacitance

Question
CBSEENPH12039798
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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 emf 2V, so as to get a potential gradient 1mV per cm on the wire is

  • 32Ω

  • 40Ω

  • 44Ω

  • 48Ω

Solution

A.

32Ω

Given, l=4m,
R= potentiometer wire resistance = 8Ω
Potential space gradient space equals space dV over dr space equals space 1 mV divided by cm So comma space for space 400 cm comma space increment straight V space equals space 400 straight x space 1 straight x 10 to the power of negative 3 end exponent space equals space 0.4 space straight V Let space straight a space resistor space straight R subscript straight s space equals space connected space in space series comma space so space as increment straight V space equals space fraction numerator straight V over denominator straight R plus straight R subscript straight s space end fraction straight x space straight R 0.4 space equals space fraction numerator 2 over denominator 8 plus straight R end fraction space straight x space 8 space rightwards double arrow 8 plus straight R equals fraction numerator 16 over denominator 0.4 end fraction space equals 40 rightwards double arrow space straight R space equals 32 space straight capital omega

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