AC and DC

Direct Current (DC)

Direct current (DC) flows in one direction only and at a constant value. Batteries and cells are DC sources. The current-time graph for a DC source is a horizontal straight line.

Alternating Current (AC)

Alternating current (AC) continuously reverses direction. The current (and voltage) follows a sinusoidal pattern with time. Mains electricity in most countries is AC, in the Caribbean this is typically 50 Hz or 60 Hz.

AC Parameters

Quantity	Symbol	Definition	Unit
Peak voltage	$V_0$	Maximum voltage in either direction	V
Peak-to-peak voltage	$2V_0$	Total voltage swing from positive to negative peak	V
Period	$T$	Time for one complete cycle	s
Frequency	$f$	Number of cycles per second; $f = 1/T$	Hz

Alternating voltage from a 50 Hz AC supply: period T = 0.02 s, peak voltage 325 V. The root-mean-square (RMS) voltage is 325/√2 ≈ 230 V, this is what appliances are rated at.

ExampleAC generator graph (2018 Paper 02, Q3)

From the voltage-time graph of an AC generator:

Peak-to-peak voltage = 20 V, so peak voltage $V_0 = 10$ V
Period read from graph: $T = 0.04$ s
Frequency: $f = \frac{1}{T} = \frac{1}{0.04} = 25 \text{Hz}$

From 2021 Paper 02, Q5b: An AC generator has a peak voltage $V_0 = 50$ V applied across a 100 Ω resistor.

Peak current: $I_0 = \frac{V_0}{R} = \frac{50}{100} = 0.5$ A

If the generator speed is doubled (frequency doubled), the period halves and the peak voltage increases (because the coil cuts field lines faster).

Half-Wave Rectification

A diode allows current to flow in only one direction. When an AC supply is connected through a diode, only one half of each AC cycle is allowed to pass. This is half-wave rectification.

Half-wave rectified output: only positive half-cycles pass through the diode. The output is always positive (DC direction) but pulsating, not smooth like a battery.

Comparison of waveforms:

Waveform	Description
DC (battery)	Constant, flat line, no variation
AC	Smooth sine wave, alternates positive and negative
Half-wave rectified AC	Positive half-cycles only; gaps where negative half-cycles were blocked

To smooth the output of a rectifier, a large capacitor is connected in parallel, it charges during peaks and discharges during gaps, reducing the variation.

Exam Tip

The period is read from the graph as the time for one complete cycle (crest to crest, or the distance from one zero crossing to the next on the same side). Frequency is $f = 1/T$ , not $T/1$ .

For AC generator questions: doubling the rotation speed doubles the frequency, halves the period, and increases the peak voltage (more EMF generated per revolution).

Alternating Current (AC)

AC Parameters

Quantity	Symbol	Definition	Unit
Peak voltage	$V_0$	Maximum voltage in either direction	V
Peak-to-peak voltage	$2V_0$	Total voltage swing from positive to negative peak	V
Period	$T$	Time for one complete cycle	s
Frequency	$f$	Number of cycles per second; $f = 1/T$	Hz

Alternating voltage from a 50 Hz AC supply: period T = 0.02 s, peak voltage 325 V. The root-mean-square (RMS) voltage is 325/√2 ≈ 230 V, this is what appliances are rated at.

ExampleAC generator graph (2018 Paper 02, Q3)

From the voltage-time graph of an AC generator:

Peak-to-peak voltage = 20 V, so peak voltage $V_0 = 10$ V
Period read from graph: $T = 0.04$ s
Frequency: $f = \frac{1}{T} = \frac{1}{0.04} = 25 \text{Hz}$

From 2021 Paper 02, Q5b: An AC generator has a peak voltage $V_0 = 50$ V applied across a 100 Ω resistor.

Peak current: $I_0 = \frac{V_0}{R} = \frac{50}{100} = 0.5$ A

If the generator speed is doubled (frequency doubled), the period halves and the peak voltage increases (because the coil cuts field lines faster).

Half-Wave Rectification

A diode allows current to flow in only one direction. When an AC supply is connected through a diode, only one half of each AC cycle is allowed to pass. This is half-wave rectification.

Half-wave rectified output: only positive half-cycles pass through the diode. The output is always positive (DC direction) but pulsating, not smooth like a battery.

Comparison of waveforms:

Waveform	Description
DC (battery)	Constant, flat line, no variation
AC	Smooth sine wave, alternates positive and negative
Half-wave rectified AC	Positive half-cycles only; gaps where negative half-cycles were blocked

To smooth the output of a rectifier, a large capacitor is connected in parallel, it charges during peaks and discharges during gaps, reducing the variation.

Exam Tip

The period is read from the graph as the time for one complete cycle (crest to crest, or the distance from one zero crossing to the next on the same side). Frequency is $f = 1/T$ , not $T/1$ .

For AC generator questions: doubling the rotation speed doubles the frequency, halves the period, and increases the peak voltage (more EMF generated per revolution).