Physics - Current Electricity Question with Solution | TestHub

A. According to the principle of potentiometer, EMF is directly proportional to the balancing length, i.e., $\mathcal{E}=kL$, where $k$ is the potential gradient. Thus, ${\mathcal{E}}_1/{\mathcal{E}}_2=L_1/L_2$.

B. At the balance point, the potential difference across the balancing length of the wire exactly equals the cell's EMF, resulting in zero current through the galvanometer.

C. The internal resistance $r_1$ can be found using the formula $r_1=R(\frac{L_1}{L^{\prime }}-1)$, where $L^{\prime }$ is the balancing length when a resistance $R$ is connected across the cell.

D. A uniform wire ensures a constant potential gradient ($k$) along its length, which is essential for accurate and reliable measurements.