UY1: Phasors & Alternating Currents

Any device that supplies a sinusoidally varying voltage (potential difference)

$$v = V \cos{\omega t}$$

, where V is the voltage amplitude,

or current

$$i = I \cos{\omega t}$$

, where I is the current amplitude,

is an alternating current (ac) source with angular frequency:

$$\begin{aligned} \omega &= 2 \pi f \\ &= \frac{2 \pi}{T} \end{aligned}$$

You can represent the information in a Phasor diagram, as shown below.

Phasor diagram

Finding the root-mean-square value for the alternating current:

$$\begin{aligned} i^{2} &= I^{2} \cos^{2}{\omega t} \\ i^{2} &= \frac{1}{2} I^{2} \left( 1 + \cos{2 \omega t} \right) \\ \frac{1}{T} \int\limits_{0}^{T} i^{2} \, dt &= \frac{1}{2} I^{2} \\ I_{\text{rms}} &= \frac{1}{\sqrt{2}} I \end{aligned}$$

A diode (rectifier) is a device that conducts better in one direction than in the other – an ideal diode has zero resistance for one direction of current and infinite resistance for the other.

For a full-wave rectifier circuit, the rectified average current is given by:

$$\begin{aligned} I_{rav} &= \frac{2}{T} \int\limits_{0}^{\frac{T}{2}} I \sin{\omega t} \, dt \\ &= \frac{4I}{\omega T} \\ &= \frac{2}{\pi} I \end{aligned}$$

Next: Resistors, Inductors & Capacitors In A.C. Circuits

Previous: R-L Circuit

Back To Electromagnetism (UY1)

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