Introduction / Context:
An inductor resists changes in current with a frequency-dependent reactance XL. In steady-state AC, the current magnitude through an ideal inductor is I = V / XL. This problem tests the ability to compute XL and the resulting rms current for given L, f, and V.
Given Data / Assumptions:
- Inductance L = 0.02 H.
- Frequency f = 100 Hz.
- Applied voltage (rms) V = 12 V.
- Ideal inductor; ignore winding resistance.
Concept / Approach:
- Inductive reactance: XL = 2 * π * f * L.
- Current magnitude: I = V / XL.
Step-by-Step Solution:
Compute XL = 2 * π * 100 * 0.02 = 2 * π * 2 = 4 * π ≈ 12.566 Ω.Compute I = 12 / 12.566 ≈ 0.955 A (rms).Therefore, the current is approximately 0.955 A.
Verification / Alternative check:
Sanity check: If L were halved, XL halves and current doubles; numbers scale as expected.
Why Other Options Are Wrong:
- 0.02 A: Would imply XL = 600 Ω, inconsistent with given f and L.
- 10 A and 2.02 A: Far too high; would require very small XL not supported by L and f.
- None of the above: Incorrect because 0.955 A matches calculation.
Common Pitfalls:
- Confusing 2 * π * f * L with 2 * π * L / f (incorrect).
- Mixing peak and rms values; V given is rms.
Final Answer:
0.955 A
Discussion & Comments