21.1 Characteristics of Alternating Currents

2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Understand and use the terms period, frequency, and peak value as applied to an alternating current or voltage.
  2. Use equations of the form x = x₀ sin ωt to represent a sinusoidally alternating current or voltage.
  3. Recall and use the fact that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current.
  4. Distinguish between root-mean-square (r.m.s.) and peak values, and use I_r.m.s. = I₀ / √2 and V_r.m.s. = V₀ / √2 for a sinusoidal alternating current.

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1. What Is Alternating Current?

In your everyday life, the electricity that comes out of a wall socket is alternating current, often written as a.c. This is different from the current that flows from a battery, which is called direct current (d.c.).

  • In direct current (d.c.), the current always flows in the same direction — like water flowing steadily one way through a pipe.
  • In alternating current (a.c.), the current continuously changes its size and periodically reverses its direction — like water sloshing back and forth. It flows one way, slows down, stops, reverses, and flows the other way, over and over again.

Because the current keeps reversing, it also means the voltage (the "push" that drives the current) keeps reversing direction too.

When we draw a graph of alternating current or voltage against time, we get a smooth wave shape called a sine wave (or sinusoidal wave). This is the most common and important shape for a.c.

2. Key Terms: Period, Frequency, and Peak Value

These three terms describe the shape and behaviour of the a.c. wave. You must know all three clearly.

2.1 Period (T)

The period is the time it takes for one complete cycle of the wave. One complete cycle means the current starts at zero, rises to its maximum in one direction, falls back to zero, rises to its maximum in the other direction, and returns to zero again — one full "wave."

  • Symbol: T
  • Unit: seconds (s) — although for mains electricity, the period is often given in milliseconds (ms)

⚠️ Exam Tip: Always check the unit on the time axis of a graph. It is very common for graphs to show time in milliseconds (ms) rather than seconds. Remember: 1 ms = 1 × 10⁻³ s. If you forget to convert, your answer will be wrong by a factor of 1000.

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