Question #42052

A potentiometer wire of length $L = 10 \text{ m}$ has a uniform potential gradient $k = 2.0 \text{ V/m}$. An unknown cell of emf $E$ is connected in the secondary circuit with a galvanometer of resistance $R_g = 25 \ \Omega$ and inductance $L_g = 2.5 \text{ H}$. The jockey is moved along the wire from $x = 0$ at a constant velocity $v = 0.4 \text{ m/s}$. An automated sensor detects the instant the galvanometer current becomes zero and applies a brake to the jockey after a mechanical processing delay of $\Delta t_m = 0.15 \text{ s}$. The brake provides a constant deceleration $a = 0.8 \text{ m/s}^2$ until the jockey stops. If the final resting position of the jockey is $x_f = 4.50 \text{ m}$, what is the true emf $E$ of the cell? (Assume the jockey starts at $t=0$ from $x=0$ and the transient effects from the start of motion have decayed).