Purely inductive AC circuit: which statement most accurately describes its opposition and phase relationship?
Computer Science
Electronic Principles
Difficulty: Easy
Choose an option
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AResistances provide the only opposition to current flow
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BInductive reactance provides the only opposition to current flow
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CCombinations of resistance and inductive reactance provide any opposition to current flow
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DThe ac voltage lags the current by 90 degree
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ENone of the above
Answer
Correct Answer: Inductive reactance provides the only opposition to current flow
Explanation
Introduction / Context:In a purely inductive circuit (ideal inductor, no resistance), the impedance is entirely imaginary and proportional to frequency. Understanding both what constitutes the opposition to current and the correct phase relationship between voltage and current is fundamental in AC analysis.
Given Data / Assumptions:
- Ideal inductor with inductance L.
- Sinusoidal steady-state operation at frequency f.
- No series or parallel resistance present.
Concept / Approach:
- Inductive reactance: X_L = 2 * π * f * L provides the opposition to current (in ohms).
- Phasor relationship: For an inductor, current lags voltage by 90°, or equivalently, voltage leads current by 90°.
Step-by-Step Reasoning:
Write impedance: Z = j X_L with X_L = 2 * π * f * L.Since R = 0, opposition is purely due to X_L.Phase: i(t) lags v(t) by 90°; therefore, any statement that voltage lags current by 90° is incorrect for an inductor.Verification / Alternative check:
From v(t) = L * di/dt, when current is at its maximum slope (crossing zero), voltage is at its peak, consistent with a 90° lead of voltage over current.Why Other Options Are Wrong:
- Resistance provides the only opposition: False for a pure inductor (R = 0).
- Combinations of R and X_L: Describes RL circuits, not purely inductive.
- Voltage lags current by 90°: Reversed; in an inductor, current lags voltage.
- None of the above: Incorrect because X_L-only opposition is correct.
Common Pitfalls:
- Mixing up inductor and capacitor phase relationships.
- Forgetting frequency dependence of X_L, which changes current magnitude.
Final Answer:
Inductive reactance provides the only opposition to current flow