Capacitive reactance current calculation: What RMS current flows through a 0.02 μF capacitor connected to a 12 V (RMS), 100 Hz AC source?

Introduction / Context:
For sinusoidal excitation, the current through a capacitor leads the voltage by 90 degrees and its magnitude depends on frequency and capacitance. Designers often use the simple product formula I = 2 * π * f * C * V to estimate AC capacitor current.

Given Data / Assumptions:

• C = 0.02 μF = 0.02 × 10^-6 F = 2 × 10^-8 F.
• V_RMS = 12 V.
• Frequency f = 100 Hz.
• Sine wave steady state.

Concept / Approach:
For a capacitor, the current magnitude is I = V * ω * C, where ω = 2 * π * f. Using RMS values for a sinusoid yields the RMS current. This avoids computing capacitive reactance first, though Xc = 1 / (2 * π * f * C) can be used equivalently with I = V / Xc.

Step-by-Step Solution:
Compute ω = 2 * π * f = 2 * π * 100 ≈ 628.318 rad/s.Multiply by C: ω * C ≈ 628.318 * 2 × 10^-8 ≈ 1.2566 × 10^-5.Multiply by V: I = 12 * 1.2566 × 10^-5 ≈ 1.508 × 10^-4 A.Convert to mA: 1.508 × 10^-4 A ≈ 0.151 mA.

Verification / Alternative check:
Compute Xc = 1 / (2 * π * f * C) ≈ 1 / (628.318 * 2e-8) ≈ 79.6 kΩ; then I = V / Xc = 12 / 79.6k ≈ 0.151 mA, consistent.

Why Other Options Are Wrong:
157 mA and 2.02 A: orders of magnitude too large; likely confusion of units.0.995 mA: would require a much larger capacitance or frequency.None: incorrect because 0.151 mA matches the calculation.

Common Pitfalls:
Misplacing decimal when converting μF to F; forgetting to use RMS voltage; mixing up radians per second with hertz.

Final Answer:
0.151 mA