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QPages 328-329: Q13: HC Verma: Concepts of Physics - Volume 2 Alternating Current Pages 328-329: Q13 Solution: A resistance is connected to an AC source. If a capacitor is…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that adding any reactive element always lowers the average power in a resistor, overlooking that series reactances add algebraically ($X_{total}=X_L-X_C$). When a small inductor follows a capacitor, it can partially cancel the capacitive reactance, reduce the total impedance, and therefore increase the current and the resistor’s average power. Always compute the net reactance before concluding the effect on power.

A resistance is connected to an AC source. If a capacitor is included in the series circuit, will the average power absorbed by the resistance increase or decrease? If an inductor of small inductance is also included in the series circuit, will the average power absorbed increase or decrease further?

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**Answer:** Decrease, then increase. **Step-by-Step Explanation:** Adding a capacitor increases the impedance Z=R2+XC2Z = \sqrt{R^2 + X_C^2}, so the current and average power Irms2RI_{rms}^2 R decrease. Adding a small inductor reduces the net reactance to ∣XC−XL∣|X_C - X_L|, decreasing the impedance and increasing the power [citation:14].

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