In the circuit, the galvanometer G shows zero deflection. If the… | JEE Main 2005 (AIEEE)

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Kirchhoff's Laws & Measuring Instruments

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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Answer: (a)

Zero deflection means no current in G, so the p.d. across R equals the 2 V of battery A.
The 12 V battery drives current through 500 $\Omega$ and R in series: $V_R = \frac{12R}{500 + R}$
$\frac{12R}{500 + R} = 2 \Rightarrow 12R = 1000 + 2R \Rightarrow R = 100\ \Omega$
So the answer is (a) $100\ \Omega$ .

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