Transformer
A transformer changes an AC voltage by mutual induction between two coils on an iron core. For an ideal one, Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ.
Construction and working
A transformer changes an alternating voltage to a higher or lower value. It has two coils, the primary (input) and the secondary (output), wound on the same soft iron core. The coils are insulated from each other and from the core. The core is made of thin laminated (layered) sheets. An alternating current in the primary produces an alternating flux in the core. This flux passes through the secondary and induces an emf in it, by mutual induction. A step-up transformer has more turns in the secondary (Nₛ > Nₚ) and raises the voltage. A step-down transformer has fewer (Nₛ < Nₚ) and lowers it. A transformer does not work on steady DC, because a constant flux induces no emf.
Deriving the turns ratio (ideal transformer)
- 1Assume: all the flux of the primary passes through the secondary (no leakage), the coil resistances are negligible, and no energy is lost.
- 2Let Φ be the flux in the core. It is the same through each turn of both coils.
- 3Emf in the secondary: εₛ = −Nₛ dΦ/dt. With negligible resistance, the output voltage vₛ = εₛ.
- 4Back emf in the primary: εₚ = −Nₚ dΦ/dt. With negligible resistance, the applied voltage vₚ = εₚ.
- 5Dividing: vₛ/vₚ = Nₛ/Nₚ.
- 6No energy loss: input power = output power, so iₚvₚ = iₛvₛ.
- 7★So, vₛ/vₚ = Nₛ/Nₚ = iₚ/iₛ. A step-up transformer raises the voltage and lowers the current in the same ratio.
★ key step
Energy losses and how they are reduced
| Loss | Cause | How it is reduced |
|---|---|---|
| Flux leakage | Some flux of the primary does not pass through the secondary | Wind the primary and secondary one over the other |
| Resistance of the windings (copper loss) | Current heats the wires (I²R) | Use thick copper wire for the coil carrying the large current |
| Eddy currents (iron loss) | The changing flux induces circulating currents in the iron core, which heat it | Use a laminated core of thin insulated sheets |
| Hysteresis | The core is magnetised and demagnetised every cycle, losing energy as heat | Use a core material with low hysteresis loss, such as soft iron |
Worked example: a step-down transformer
A transformer steps 220 V down to 11 V for a doorbell. Its primary has 2000 turns. (a) How many turns does the secondary have? (b) If the secondary current is 2 A, find the primary current, assuming the transformer is ideal.
- (a) Nₛ/Nₚ = Vₛ/Vₚ, so Nₛ = Nₚ × Vₛ/Vₚ = 2000 × 11/220.
- 11/220 = 1/20, so Nₛ = 2000 ÷ 20 = 100 turns.
- (b) Ideal transformer: VₚIₚ = VₛIₛ.
- Iₚ = VₛIₛ/Vₚ = 11 V × 2 A ÷ 220 V = 22 ÷ 220 = 0.1 A.
- Check: power in = 220 V × 0.1 A = 22 W; power out = 11 V × 2 A = 22 W.
(a) 100 turns; (b) 0.1 A
Worked example: why power is sent at high voltage
A power station sends 100 kW to a town through lines of total resistance 5 Ω. Compare the power lost in the lines when it is sent at 1000 V and when it is first stepped up to 10,000 V.
- At 1000 V: I = P/V = 100,000 W ÷ 1000 V = 100 A.
- Loss = I²R = (100 A)² × 5 Ω = 50,000 W = 50 kW, half the power sent.
- At 10,000 V: I = 100,000 W ÷ 10,000 V = 10 A.
- Loss = (10 A)² × 5 Ω = 500 W = 0.5 kW.
- Raising the voltage 10 times cuts the current 10 times and the loss 100 times. So power is sent at high voltage and stepped down near homes.
50 kW lost at 1000 V; only 0.5 kW lost at 10,000 V
How to draw a transformer
- Draw the soft iron core as a thick square frame, with a few parallel lines across it to show the laminations.
- Wind the primary coil on the left limb and label Nₚ, Vₚ and Iₚ.
- Wind the secondary coil on the right limb (more loops for step-up, fewer for step-down) and label Nₛ, Vₛ and Iₛ.
- Join an AC source (a circle with a ~ sign) to the primary and a load R to the secondary.
- Draw arrows round the core to show the alternating flux Φ.
- Write the title: step-up (or step-down) transformer. You may also show the two coils wound one over the other on the same limb.
The grey distribution transformer on a pole or platform in your street steps the line voltage down to 220 V for homes. Many mobile chargers also have a small transformer inside them.
5 marks: “Explain the principle, construction and working of a transformer with a labelled diagram. Derive the relation between the voltages and the numbers of turns. Give two causes of energy loss and how each is reduced.” Mutual induction; core, primary and secondary; vₛ/vₚ = Nₛ/Nₚ from ε = −N dΦ/dt; ideal iₚvₚ = iₛvₛ; losses: flux leakage, copper loss, eddy currents (laminated core), hysteresis (any two with remedies).
2 marks: “A step-up transformer changes 230 V to 2300 V. Its primary has 50 turns. Find the number of secondary turns and the current ratio Iₛ/Iₚ for an ideal transformer.” Nₛ = 50 × 2300/230 = 500 turns; Iₛ/Iₚ = Nₚ/Nₛ = 1/10.
1 marks: “Why can a transformer not be used to step up a steady DC voltage?” A steady DC gives a constant flux, which induces no emf in the secondary.
Turns ratio rules: Vₛ/Vₚ = Nₛ/Nₚ. Voltage goes up, current goes down, and power stays the same (ideal).