AC signals and reactance: peak, peak-to-peak and RMS values, frequency and period, capacitive and inductive reactance, and the phase relationship between voltage and current.

What this dot point is asking

Alternating signals behave differently from DC because capacitors and inductors oppose them in a frequency-dependent way. WJEC expects you to describe AC signals using peak, peak-to-peak and RMS values, relate frequency and period, calculate capacitive and inductive reactance, and state how each varies with frequency and the phase between voltage and current. RMS and reactance calculations underpin the whole filter topic and recur in the exam.

The answer

Describing an AC signal

The RMS value matters because it determines the power delivered: an AC supply quoted as 230 V is the RMS value, with a peak of about 325 V.

Capacitive reactance

Reactance is the AC opposition (in ohms) of a capacitor. Because $X_C$ is inversely proportional to frequency, a capacitor passes high frequencies and blocks low frequencies and DC (at DC, $f = 0$, the reactance is infinite, so no current flows once charged).

Inductive reactance

An inductor's reactance is proportional to frequency, so it blocks high frequencies and passes low frequencies and DC. This opposite behaviour to a capacitor is what lets the two be combined to select frequency bands.

Phase

Examples in context

Example 1. Smoothing a power supply

A large capacitor across a rectified supply has a low reactance to the high-frequency ripple but a high reactance to the slow DC level, so it shunts the ripple to ground while holding the DC. The frequency dependence of $X_C$ is what makes the reservoir capacitor smooth the output.

Example 2. A DC-blocking coupling capacitor

Between amplifier stages, a capacitor passes the AC signal (low reactance at signal frequencies) but blocks the DC bias (infinite reactance at DC). This is why coupling capacitors couple signal without disturbing each stage's operating point.

Example 3. RMS and real power

A heater rated at 230 V AC delivers the same average power as a 230 V DC supply because the RMS value is defined to give equal heating. Using the peak (325 V) instead would overstate the power by a factor of two, which is why power calculations always use RMS.

Try this

Q1. A sine wave has an RMS voltage of $10\,\text{V}$. Find its peak voltage. [2 marks]

• Cue. $V_{peak} = V_{rms} \times \sqrt{2} = 10 \times 1.414 = 14.1\,\text{V}$.

Q2. State whether a capacitor or an inductor passes DC, and explain in terms of reactance. [2 marks]

• Cue. An inductor passes DC: at $f = 0$, $X_L = 2\pi f L = 0$. A capacitor blocks DC: at $f = 0$, $X_C = \frac{1}{2\pi f C}$ is infinite.