A hot wire voltmeter measures the voltages across the inductor, the capacitor and the resistor as 150 V, 100 V and 50 V across a series, LCR circuit. If resistance is \( 100\,\Omega \), the current in the circuit is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 0.5\,\mathrm{A} \)
In a series circuit the same current flows through L, C and R, and the voltage across the resistor is in phase with it. A hot wire voltmeter reads rms values, so Ohm’s law for the resistor gives the current directly:
\( \displaystyle I = \frac{V_R}{R} = \frac{50\,\mathrm{V}}{100\,\Omega} = 0.5\,\mathrm{A} \)
Check with the other readings: \( X_L = 150/0.5 = 300\,\Omega \) and \( X_C = 100/0.5 = 200\,\Omega \), so \( Z = \sqrt{100^{2} + (300-200)^{2}} \approx 141\,\Omega \) and the supply voltage is \( IZ \approx 70.7\,\mathrm{V} = \sqrt{V_R^{2} + (V_L - V_C)^{2}} \), because \( V_L \) and \( V_C \) are in opposite phase.