Capacitative AC circuit

Electricity and Magnetism Level 2

A $200 \mu\text{F}$ capacitor is attached to $10 \text{ V}$ AC source. What is the RMS current at a frequency of $\dfrac{500}{\pi} \text{ Hz}?$

2 \mu\text{A}

2 \text{ mA}

200 \text{ A}

2 \text{ A}

1 solution

Tom Engelsman
Nov 30, 2016

Using Ohm's Law with capacitive impedance, we have the relationship $V = |Z_c|*I$ where $|Z_c| = |\frac{1}{j\omega*C}| = |-\frac{j}{\omega*C}| = \frac{1}{\omega*C}$ . Solving for the current, we obtain:

$I = VC\omega = VC(2\pi f) = (10 V)(200 \mu F)(2\pi * \frac{500}{\pi} Hz) = \boxed{2 A}$ .

Capacitative AC circuit

1 solution

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