Alternating Current

DC (Direct Current): Current flows in one direction. Constant value.

AC (Alternating Current): Current and voltage oscillate sinusoidally:

$V = V_0 \sin(\omega t)$ $I = I_0 \sin(\omega t)$

Where $V_0$, $I_0$ = peak values; $\omega = 2\pi f$.

UK mains: $f = 50$ Hz, $V_{\text{rms}} = 230$ V.

The root mean square value of an AC quantity gives the equivalent DC value that would dissipate the same power in a resistor.

$\boxed{V_{\text{rms}} = \frac{V_0}{\sqrt{2}}}$ $\boxed{I_{\text{rms}} = \frac{I_0}{\sqrt{2}}}$

Power in AC

$P = I_{\text{rms}} V_{\text{rms}} = I_{\text{rms}}^2 R = \frac{V_{\text{rms}}^2}{R}$

The average power = half the peak power: $P_{\text{avg}} = \frac{1}{2}V_0 I_0 = \frac{1}{2}I_0^2 R$

• Y-axis: Voltage (read amplitude = peak value)
• X-axis: Time (read period → calculate frequency)
• Peak-to-peak = $2V_0$
• $f = 1/T$

Half-wave rectification: A single diode blocks the negative half-cycle.

Full-wave rectification: A bridge rectifier (4 diodes) flips negative half-cycles to positive.

Smoothing: A capacitor across the output fills in the gaps, providing nearly DC. Larger capacitance = smoother output.

• $V_{\text{rms}} = V_0/\sqrt{2}$; $I_{\text{rms}} = I_0/\sqrt{2}$
• Power: use rms values (equivalent DC)
• Oscilloscope: read peak and period directly
• Rectification: half-wave (1 diode) or full-wave (bridge); smoothed with capacitor