In the circuit shown, a four wire potentiometer is made of a 400 cm long wire, which extends between $A$ and $B$. The resistance per unit length of the potentiometer wire is $r = 0.01 \Omega / \mathrm{cm}$. If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be:

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Current Electricity

In the circuit shown, a four wire potentiometer is made of a 400 cm long wire, which extends between

A

and

B

. The resistance per unit length of the potentiometer wire is

r = 0.01Ω/ cm

. If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be:

Answer: (C)

The whole potentiometer wire AB has resistance

R_{A B} = 400 cm \times 0.01 Ω/ cm = 4 Ω

. With the

2 Ω

already in the loop, the circuit carries

i = \frac{3 V}{2 + 4} = 0.5 A

. The voltmeter reads the drop across the stretch from A to the jockey at

50 cm

, whose resistance is

R_{A J} = 50 cm \times 0.01 Ω/ cm = 0.5 Ω

. So the reading is

V = i R_{A J} = 0.5 A \times 0.5 Ω = 0.25 V

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option