Question

A potential difference of 220 V is maintained across a 12000 ohm rheostat, as shown
in the figure. The voltmeter has a resistance of 6000 ohm and point c is at one-fourth
of the distance from a to b. Therefore, the reading of the voltmeter will be
(c) 32 V
(d) 36 V
(a) 40 V
(b) 42 V​

Answer 1

Answer:

Explanation:

=> As in case of linear rheostat R ∝ length L.

R_AC / R_AB = AC/AB

But R_AB = 12000 Ω

and AC = 1/4 AB

∴ R_AC = 12000 * 1/4

= 3000 Ω

=> As the resistance R_AC (= 3000 Ω) is in parallel with voltmeter of resistance of 6000 Ω. Therefore, the effective resistance between points A and C will be

R'_AC = 3000 * 6000 / ( 3000 + 6000)

= 2000 ohm

=> Resistance between points B and C

=> R_BC and R'_AC are in series. Therefore, the voltmeter reading will be

V_AC = R'_AC V_AB / (R_BC + R'_AC)

= 2000 / (9000 + 2000) * 220

= 2000 * 220 / 11000

= 440000 / 11000

= 40 V

Thus, the reading of the voltmeter will be 40 V