Ideal inductor power concept: For a pure (ideal) inductor driven by a sinusoidal source, how does average power dissipation relate to operating frequency?
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APower dissipation decreases as frequency increases
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BPower dissipation is maximum at DC source voltages
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CPower dissipation increases as frequency increases
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DThere is no meaningful relationship (ideal inductor has zero average power at any frequency)
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ENone of the above
Answer
Correct Answer: There is no meaningful relationship (ideal inductor has zero average power at any frequency)
Explanation
Introduction / Context:This question distinguishes reactive energy storage from real power dissipation. In AC circuits, inductors and capacitors exchange energy with the source but do not dissipate average power if they are ideal (no resistance). Understanding this helps in power factor correction and reactive component selection.
Given Data / Assumptions:
- Inductor is ideal: no series resistance, no core losses.
- Source is sinusoidal steady state.
- We ask about average (real) power, not instantaneous energy exchange.
Concept / Approach:For a pure inductor, voltage and current are 90 degrees out of phase. Instantaneous power p(t) = v(t) * i(t) is alternating positive and negative; the average over a full cycle is zero. Frequency changes the reactive impedance X_L = 2 * pi * f * L, affecting current magnitude for a given voltage, but average real power in the ideal case remains zero regardless of frequency.
Step-by-Step Solution:Use X_L = 2 * pi * f * L to see current scaling with frequency.Recognize phase shift: current lags voltage by 90 degrees in an ideal inductor.Average real power = 0 for ideal reactive elements; only reactive power oscillates.Hence, no “increasing” or “decreasing” trend with frequency for average dissipation.
Verification / Alternative check:Include small series resistance R_s for realism: P_avg ≈ I^2 * R_s. Here, frequency affects I via X_L, but the strictly ideal component has R_s = 0, giving P_avg = 0 at any f.
Why Other Options Are Wrong:(a) and (c) claim a monotonic trend; not true for an ideal inductor's average power. (b) DC through an ideal inductor after transients yields zero voltage drop and zero power. (e) Invalid since a correct statement exists.
Common Pitfalls:Confusing reactive power with real power; assuming frequency dependence of current equates to power loss; ignoring non-ideal resistive effects.
Final Answer:There is no meaningful relationship (ideal inductor has zero average power at any frequency).