Question:
A resistor of resistance 30 $\Omega$ and a capacitor of reactance 40 $\Omega$ are connected in series to an ac supply. If the rms current through the resistor is 2 mA, then the wattless current is:
A resistor of resistance 30 $\Omega$ and a capacitor of reactance 40 $\Omega$ are connected in series to an ac supply. If the rms current through the resistor is 2 mA, then the wattless current is:
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Wattless current is the component of current that does not contribute to average power dissipation.
Updated On: Jun 10, 2026
- Zero
- 2 mA
- 1.2 mA
- 1.6 mA
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The Correct Option is B
Solution and Explanation
Step 1: Concept
In an RC circuit, the total current $I_{rms}$ is the same through both components. Wattless current is $I_{rms} \sin \phi$.
Step 2: Analysis
Impedance $Z = \sqrt{R^2 + X_c^2} = \sqrt{30^2 + 40^2} = 50$ $\Omega$. $\sin \phi = X_c / Z = 40 / 50 = 0.8$. $I_{wattless} = I_{rms} \cdot \sin \phi = 2 \text{ mA} \times 0.8 = 1.6 \text{ mA}$? Re-evaluating: In a series circuit, $I$ is constant. Wattless current refers to the component of $I$ through the reactive component.
Final Answer: (D)
In an RC circuit, the total current $I_{rms}$ is the same through both components. Wattless current is $I_{rms} \sin \phi$.
Step 2: Analysis
Impedance $Z = \sqrt{R^2 + X_c^2} = \sqrt{30^2 + 40^2} = 50$ $\Omega$. $\sin \phi = X_c / Z = 40 / 50 = 0.8$. $I_{wattless} = I_{rms} \cdot \sin \phi = 2 \text{ mA} \times 0.8 = 1.6 \text{ mA}$? Re-evaluating: In a series circuit, $I$ is constant. Wattless current refers to the component of $I$ through the reactive component.
Final Answer: (D)
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