For what value of resistance R in the given c | vedclass

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(B) For the galvanometer reading to be zero,the potential difference across the resistor $R$ must be equal to the electromotive force $(EMF)$ of the b

Vedclass · Accepted Answer

$100$

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(B) For the galvanometer reading to be zero,the potential difference across the resistor $R$ must be equal to the electromotive force $(EMF)$ of the battery in the right branch,which is $2 \ V$.The total voltage in the left branch is $12 \ V$. Since the galvanometer shows zero deflection,no current flows through the right branch. Thus,the current $I$ flows only through the $500 \ \Omega$ resistor and the resistor $R$ in series.The potential difference across the $500 \ \Omega$ resistor is $12 \ V - 2 \ V = 10 \ V$.The current flowing through the circuit is $I = \frac{10 \ V}{500 \ \Omega} = \frac{1}{50} \ A$.Since the potential difference across resistor $R$ is $2 \ V$,we have $V_R = I 	imes R$.$2 \ V = (\frac{1}{50} \ A) 	imes R$$R = 2 	imes 50 \ \Omega = 100 \ \Omega$.

For what value of resistance $R$ in the given circuit will the galvanometer reading be zero (in $\Omega$)? The internal resistance of both batteries is negligible.

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