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  4. In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be

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Q. In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will bePhysics Question Image

Jharkhand CECEJharkhand CECE 2008

Solution:

The galvanometer shows zero deflection ie, current through XY is zero.
As a result potential drop across R is 2 V, circuit can be redrawn as
$ I=\frac{12}{500+R} $
Voltage across $ R,V=IR $
$ \Rightarrow $ $ 2=\frac{12}{500+R}\times R $
$ \Rightarrow $ $ 1000+2R=12R\Rightarrow R=100\,\Omega $

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