Question

A voltmeter is connected across a 400Ω resistance and reads 30 volt. If the same voltmeter is connected across the 300Ω resistance, then its reading will be

(1) 30 volt

(2) 22.5 volt

(3) 24 volt

(4) (90/7) volt

Answer 1

(2) 22.5 volt

Let Rv be the resistance of the voltmeter. Then Rv and 400Ω resistance, when connected in parallel would have an equivalent resistances given by

and the current in the circuit with correspond to

According to question potential drop across AB is 30 volt so

Solving we obtain R_v = 1200Ω

Now when the voltmeter is connected across 300Ω the equivalent resistance of their parallel combination, is

Now the total resistance of the circuit would be (240+400)Ω = 640Ω and the corresponding current is (60/640)

Hence in this case reading of the voltmeter would be

60/640 x 240 = 22.5 Volt.