A-Level Physics: AC Theory, RMS Voltages – and Why 230 V Isn’t 230 V at All

 A-Level Physics: AC Theory, RMS Voltages – and Why 230 V Isn’t 230 V at All

When students first meet alternating current in A-Level Physics, there’s a moment of quiet confusion:

“If the UK mains supply is 230 V… why does the graph go above 230 V?”

Excellent question.

Because 230 V isn’t the peak voltage. It isn’t even the average voltage. It’s something called the RMS voltage — and that changes everything.

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1️⃣ What Is AC?

In the UK, our mains electricity is:

• Alternating Current (AC)

• Frequency = 50 Hz

• Stated voltage = 230 V

Unlike DC (direct current), AC voltage:

• Continuously changes direction

• Follows a sine wave

• Alternates between positive and negative values

Mathematically:

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

Where:

• $V_0$ = peak voltage

• $\omega$ = angular frequency

• $t$ = time

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2️⃣ Peak Voltage vs RMS Voltage

Here’s the key idea students must master:

$$V_{RMS} = \frac{V_0}{\sqrt{2}}$$

So if the RMS voltage is 230 V:

$$V_0 = 230 \times \sqrt{2}$$ $$V_0 \approx 325 \text{ V}$$

🚨 That means the UK mains actually reaches +325 V and –325 V every cycle.

Not 230 V.

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3️⃣ So What Does RMS Actually Mean?

RMS stands for:

Root Mean Square

It is the DC voltage that would produce the same heating effect in a resistor.

This is crucial.

Because power in a resistor is:

$$P = \frac{V^2}{R}$$

If we simply averaged the AC voltage over a full cycle, we'd get zero (positive and negative cancel).

But heating depends on V², which is always positive.

So we:

1. Square the voltage

2. Find the mean

3. Take the square root

Hence: Root Mean Square.

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4️⃣ Why Engineers Use RMS

Imagine a 230 V electric heater.

If we replaced AC with DC, the DC voltage that would produce the same heating effect is:

$$230\text{ V DC}$$

That’s why appliances are rated using RMS values.

It allows fair comparison between AC and DC power delivery.

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5️⃣ Common Exam Mistakes

From years of teaching A-Level Physics, these errors appear again and again:

❌ Confusing peak and RMS
❌ Forgetting the √2 factor
❌ Using 230 V as peak in power calculations
❌ Forgetting RMS current obeys the same rule:

$$I_{RMS} = \frac{I_0}{\sqrt{2}}$$

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6️⃣ Why This Matters Beyond the Exam

Understanding RMS is vital for:

• Designing power supplies

• Understanding transformers

• Working with oscilloscopes

• Safety calculations

• Interpreting energy transfer

It also explains why touching a “230 V” supply is far more dangerous than students imagine — because the peaks are significantly higher.

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7️⃣ A Quick Exam-Style Question

The UK mains supply is 230 V RMS.

a) Calculate the peak voltage.
b) Calculate the peak current if a 2 kW heater is connected.

(Hint: Start with $P = VI$ using RMS values.)

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Final Thought

AC theory is one of those topics that feels abstract — until you realise your entire house is powered by a sine wave swinging between +325 V and –325 V fifty times every second.

Suddenly it feels rather more real.