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QPages 328-329: Q9: HC Verma: Concepts of Physics - Volume 2 Alternating Current Pages 328-329: Q9 Solution: A current passes through a resistor of resistance R. How much…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat power $P=I^2R$ as a linear quantity and add the powers from two opposite sinusoidal currents, concluding a non‑zero heat; remember that power depends on the square of the total current, so when $i_1$ and $i_2$ are present together the net current is zero and the heat produced is zero.

A current i1=i0sin⁡ωti_1 = i_0 \sin \omega t passes through a resistor of resistance R. How much thermal energy is produced in one time period? A current i2=−i0sin⁡ωti_2 = -i_0 \sin \omega t passes through the resistor. How much thermal energy is produced in one time period? If i1i_1 and i2i_2 both pass through the resistor simultaneously, how much thermal energy is produced? Is the principle of superposition obeyed in this case?

Step-by-Step Verified Solution

**Answer:** (a) i02Rπω\frac{i_0^2 R \pi}{\omega} (b) Same (c) Zero (d) Yes. **Step-by-Step Explanation:** For i1=i0sin⁡ωti_1 = i_0 \sin \omega t, the thermal energy over one period is H=Irms2RT=i022R2πω=i02RπωH = I_{rms}^2 R T = \frac{i_0^2}{2} R \frac{2\pi}{\omega} = \frac{i_0^2 R \pi}{\omega}. The same result holds for i2=−i0sin⁡ωti_2 = -i_0 \sin \omega t. If both pass simultaneously, the net current is zero, so no heat is produced. The superposition principle is obeyed for the currents, but not for the power [citation:14][citation:16].

All Questions in this Chapter

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