This physics grades 11-12 lesson on transformers notes gives the key ideas first, then worked examples and diagrams. After that, practise with the worksheet on transformers and check yourself with the quiz.
Quick answer: An alternating current reverses direction regularly, and its rms value, V₀/√2 for a sine wave, gives the equivalent steady heating effect. A transformer uses electromagnetic induction to change the voltage in the ratio Vs/Vp = Ns/Np. Transmitting power at high voltage reduces the current and so the I²R loss in cables.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 3.7.5
Transformers notes: the key ideas
What is alternating current and what are rms values?
In direct current the charges drift one way. In alternating current (ac) they swing back and forth, and the voltage follows a sine wave. Mains electricity in the UK, India, Pakistan, Nigeria and Kenya alternates 50 times per second, while Texas and most of the Americas use 60 Hz.
A voltage that is positive half the time and negative half the time has an average of zero, so we use a more useful measure that tells us the heating effect.
The root mean square (rms) value of an alternating voltage or current is the value of the direct voltage or current that would deliver the same average power to a resistor. For a sine wave, Vrms = V₀ / √2 and Irms = I₀ / √2, where V₀ and I₀ are the peak values.
P = Vrms Irms = Irms² R = Vrms² / R
P = mean power (W), Vrms = rms voltage (V), Irms = rms current (A), R = resistance (Ω). The frequency is f = 1/T, and ω = 2πf.
A kettle is rated 2.3 kW on a 230 V rms supply. Calculate the peak voltage, the rms current and the resistance.
V₀ = √2 × 230 = 325 V. Irms = P/V = 2300 / 230 = 10 A. R = V/I = 230 / 10 = 23 Ω.
How does a transformer work?
A transformer has two coils wound on a shared soft iron core. The alternating primary current produces a changing flux in the core, and by Faraday’s law this induces an alternating emf in the secondary coil. It only works with ac, because a steady flux induces nothing.
Vs / Vp = Ns / Np. For an ideal transformer there is no power loss, so VpIp = VsIs. More secondary turns gives a step-up transformer; fewer gives a step-down transformer.
A phone charger transformer has 920 primary turns and operates from 230 V. It needs a 12 V secondary. Calculate the secondary turns and, for a 30 W load, the primary current if the transformer is ideal.
Ns = Np Vs/Vp = 920 × 12 / 230 = 48 turns. Ip = P/Vp = 30 / 230 = 0.13 A.
Why is electricity transmitted at high voltage?
The power lost as heat in a cable of resistance R is I²R. For a given power P = VI, raising the voltage lowers the current, so the loss falls with the square of the current. Transformers make this possible, because they change voltage cheaply and efficiently.
A farm cooperative sends 20 kW through cables of total resistance 2.0 Ω. Compare the loss at 400 V and at 8000 V.
At 400 V: I = 20 000 / 400 = 50 A, loss = I²R = 50² × 2.0 = 5000 W (25 %). At 8000 V: I = 20 000 / 8000 = 2.5 A, loss = 2.5² × 2.0 = 12.5 W (0.063 %).
What makes a real transformer lose energy?
| Loss | Cause | Reduced by |
|---|---|---|
| Heating of coils | resistance of the wire | thick copper wire |
| Eddy currents | currents induced in the core | laminated iron core |
| Hysteresis | core magnetising and demagnetising | soft iron that magnetises easily |
| Flux leakage | not all flux links both coils | winding coils on top of each other |
Students quote the peak voltage as “the mains voltage”. A mains supply of 230 V is an rms value, so its peak is 325 V.
A step-up transformer raises the voltage but lowers the current by the same factor. You never get more power out than you put in, so always check Vp × Ip against Vs × Is.
- V_rms = V₀/√2 and I_rms = I₀/√2 for a sine wave.
- Mean power P = V_rms I_rms = I_rms² R.
- Ideal transformer: Vs/Vp = Ns/Np and Vp Ip = Vs Is.
- Power loss in cables: P = I²R, so high voltage means low loss.
- Transformers need ac, laminated iron cores and thick copper windings.
Rms values, transformers and power lines: frequently asked questions
What does rms stand for and why is it used?
Rms means root mean square. It gives the steady value that would heat a resistor equally, so it lets us compare ac with dc in power calculations.
Why does a transformer not work on direct current?
A direct current gives a constant flux, so Faraday’s law gives no induced emf in the secondary. Only a changing flux induces an emf.
Why does a step-up transformer not give more power?
Energy is conserved. Raising the voltage lowers the current by the same factor, so the output power cannot exceed the input power.
Why are transformer cores laminated?
The thin insulated sheets break up the paths of eddy currents in the iron, which reduces heating and wasted energy.
What is the peak voltage of 230 V mains?
The peak voltage is √2 × 230 V, which is about 325 V. The 230 V figure is the rms value.
