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Question #42305

Difficulty: 8/10 | 🟢 Free

The Question

An alternating voltage $V(t) = 200 \sin(\omega t) + 100 \sin(3\omega t)$ is applied across a complex circuit element. The resulting current through the circuit is measured to be $I(t) = 10 \sin(\omega t - \frac{\pi}{3}) + 5 \sin(2\omega t) + 5\sqrt{2} \sin(3\omega t - \frac{\pi}{4})$ . All quantities are in SI units. What is the average power dissipated in the circuit over a long time?

Options

A.
$750\text{ W}$
B.
$500\text{ W}$
C.
$1500\text{ W}$
D.
$1000 + 250\sqrt{2}\text{ W}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Dot Product Geometry|Power Factor Definition|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of power dissipation in AC circuits with non-sinusoidal, multi-harmonic signals.

A common trap is attempting to calculate an overall root-mean-square voltage and current to apply a single power factor, or incorrectly assuming that cross-frequency terms contribute to the average power.

By forcing the use of the superposition of Fourier components, it highlights the orthogonality of harmonics: only voltage and current components of the exact same frequency can produce a non-zero time-averaged power.

Students who ignore this principle will either calculate apparent power, ignore the phase shifts, or incorrectly sum amplitudes.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Dot Product Geometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free