Two resistors of 100Ω each are connected in series with a 9 V battery. A voltmeter of 400Ω resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ___

Two resistors of 100Ω each are connected in series with a 9 V battery

Q. Two resistors of 100Ω each are connected in series with a 9 V battery. A voltmeter of 400Ω resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ____ V.

(A) 3

(B) 2

(D) 4.5

Correct Answer: 4

Explanation

Each resistor has resistance 100Ω. The voltmeter of resistance 400Ω is connected across one of the 100Ω resistors.

Equivalent resistance of the resistor and voltmeter in parallel:

\[ R_p = \frac{100 \times 400}{100 + 400} = \frac{40000}{500} = 80\ \Omega \]

This parallel combination is in series with the other 100Ω resistor.

\[ R_{\text{total}} = 100 + 80 = 180\ \Omega \]

Total current in the circuit:

\[ I = \frac{V}{R_{\text{total}}} = \frac{9}{180} = 0.05\ \text{A} \]

Voltage across the parallel combination (and hence across the voltmeter):

\[ V = I \times R_p = 0.05 \times 80 = 4\ \text{V} \]

Therefore, the voltmeter reading is 4 V.

Explanation

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