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The galvanometer deflection, when key $$K_1$$ is closed but $$K_2$$ is open, equals $$\theta_0$$ (see figure). On closing $$K_2$$ also and adjusting $$R_2$$ to $$5\Omega$$, the deflection in galvanometer becomes $$\frac{\theta_0}{5}$$. The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]:
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