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(C) The circuit is a balanced Wheatstone bridge because the galvanometer shows no deflection.Let $R_1$ be the equivalent resistance of the parallel co

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$12$

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(C) The circuit is a balanced Wheatstone bridge because the galvanometer shows no deflection.Let $R_1$ be the equivalent resistance of the parallel combination of $x \ \Omega$ and $6 \ \Omega$,and $R_2 = 2 \ \Omega$.Let $R_3 = 6 \ \Omega$ and $R_4 = 3 \ \Omega$.For a balanced bridge,the condition is $\frac{R_1}{R_2} = \frac{R_3}{R_4}$.Here,$R_1 = \frac{x \cdot 6}{x + 6}$.Substituting the values: $\frac{\frac{6x}{x+6}}{2} = \frac{6}{3}$.$\frac{6x}{2(x+6)} = 2$.$\frac{3x}{x+6} = 2$.$3x = 2x + 12$.$x = 12 \ \Omega$.

The galvanometer shows no deflection. What is the value of the resistance $x$ in $\Omega$?

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