Measuring Devices ( Galvanometer, Voltmeter and Ammeter & Meter Bridge ): Practice Problem & Solution
A potentiometer wire of length $L$ and a resistance $r$ are connected in series with a battery of e.m.f. $E_0$ and a resistance $r_1$. An unknown e.m.f. $E$ is balanced at a length $l$ of the potentiometer wire. The e.m.f. $E$ will be given by: (2015 Re)
Solution Explained:
To solve this problem, we apply the core principles of Measuring Devices ( Galvanometer, Voltmeter and Ammeter & Meter Bridge ). Understanding the underlying formula is key to arriving at the correct answer below:
Current through the potentiometer wire is $I = \frac{E_0}{r + r_1}$.
Potential gradient is $k = \frac{I r}{L} = \frac{E_0 r}{(r + r_1) L}$.
The unknown e.m.f. $E = k \cdot l = \frac{E_0 r}{(r + r_1)} \frac{l}{L}$.
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