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The driver cell of a potentiometer has an e.m.f. of 2 V and negligible internal resistance. The potentiometer wire has a resistance of 3 Ω. Calculate the resistance needed in series with the wire if a p.d. of 1.5 mV is required across the whole wire.

Given,
Emf (E)=2V
Resistance of Potentiometer wire (R)=3Ω
Potential Difference (V)=1.5mV=1.5103V
Let, R be the resistance to be connected in series.
Total resistance of the circuit (RT)=R+3
Here, current across the potentiometer circuit (I)=ERT=2R+3
Also, we have, p.d. across potentiometer wire =IR
or, 1.5103=2R+33
or, R+3=4000
R=3997Ω
Hence resistance needed in series =3997Ω
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