Capacitors in AC Circuits

In a capacitor in a dc circuit, charge flows until the capacitor is charged. In an ac circuit with a capacitor, charge flows continuously because the direction of flow changes.

The rms voltage across a capacitor is given by, V rms = I rms X C. X C is the capacitive reactance. X C = 1/ (2π f C)

Ex. 1 - The capacitance of a circuit’s capacitor is 1.50 µF, and the rms voltage of the generator is 25.0 V. What is the rms current in the circuit when the frequency of the generator is: (a) 1.00 x 10 2 Hz and (b) 5.00 x 10 3 Hz?

Instantaneous current in an ac circuit resistance is in phase with the instantaneous voltage. This in phase relationship does not exist for a capacitor in an ac circuit.

Voltage and current are one-quarter wave cycle out of phase. The voltage fluctuates as V 0 sin (2π ft). The current varies as I 0 sin (2πft + π/2) = I 0 cos (2πft).

The current in a capacitor leads the voltage across the capacitor by a phase angle of 90°. At some points, the voltage or current are negative, and that makes the power negative.

On the average, the power is zero and a capacitor uses no energy in an ac circuit.

Inductors in AC Circuits

An inductor is usually a coil of wire. It develops a voltage that opposes a change in the current, V = -L(∆I/∆t). Across an inductor, the rms voltage is: V rms = I rms X L. X L is the inductive reactance. X L = 2πfL

Ex. 2 - A circuit contains a 3.60 mH inductor. The rms voltage of the generator is 25.0 V. Find the rms current in the circuit when the generator frequency is (a) 1.00 x 10 2 Hz and (b) 5.00 x 10 3 Hz.

In an inductor ac circuit, the current reaches maximum after the voltage does. It is said that the current lags behind the voltage by a phase angle of 90°.

An inductor alternately absorbs and releases energy, so on the average, the power is zero and an inductor uses no energy in a circuit.