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A voltmeter reads 20 V and an ammeter reads 5 A in a circuit. The internal resistances of the voltmeter and ammeter are 10 kΩ and 0.2 Ω respectively. Find the value of the resistance R (in Ω).

1. 3.8 Ω
2. 4 Ω
3. 4.2 Ω
4. 3.6 Ω

Correct answer: 3.8 Ω

Solution

The voltmeter (10 kΩ) is across R, so voltage across R is 20 V. The ammeter carries 5 A; voltage across ammeter = 5 × 0.2 = 1 V. Total EMF = 21 V, but voltage across R = total voltage minus ammeter drop = 5(R + 0.2) = 20, giving R = 3.8 Ω.

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