A four-wire potentiometer is made of a $400\ \text{cm}$ long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is $r = 0.01\ \Omega/\text{cm}$. The wire is connected in series with a $1\ \Omega$ resistor and two cells, each of emf $1.5\ \text{V}$ and internal resistance $0.5\ \Omega$. If an ideal voltmeter is connected between end A and a jockey J placed at $50\ \text{cm}$ from end A (along the wire), the expected reading of the voltmeter will be
Answer: (B) $0.25\ \text{V}$
Resistance of the whole wire: $400\times0.01 = 4\ \Omega$. Total resistance in the circuit: $4 + 1 + 0.5 + 0.5 = 6\ \Omega$; total emf $3\ \text{V}$.
$$I = \frac36 = 0.5\ \text{A}$$
The ideal voltmeter draws no current, so it reads the drop across $50\ \text{cm}$ of wire ($0.5\ \Omega$):
$$V = 0.5\times0.5 = 0.25\ \text{V}$$
Solution by Sreeraj P, M.Sc Physics