A transformer changes an alternating voltage using two coils on a shared iron core. The ratio of the voltages equals the ratio of the turns.
This lesson is part of SPM Physics electromagnetism. It depends on explaining electromagnetic induction.
What are the relationships?
For an ideal transformer, these two equations are all you need.
- Voltage and turns: Vₛ ÷ Vₚ = Nₛ ÷ Nₚ
- Power: VₚIₚ = VₛIₛ
Write the primary and secondary values in a small table before you calculate. Then decide whether the answer should be bigger or smaller than the input.
Worked example: a step-down transformer
A transformer has 1200 turns on the primary and 60 on the secondary. The primary is connected to 240 V a.c.
- Sense check: the secondary has fewer turns, so the voltage is smaller.
- Vₛ = 240 × (60 ÷ 1200) = 240 × 0.05 = 12 V.
Suppose the secondary supplies 2.0 A at 12 V. The output power is 12 × 2.0 = 24 W. For an ideal transformer, the primary current is 24 ÷ 240 = 0.10 A.
If a real transformer needs 30 W at the input, its efficiency is (24 ÷ 30) × 100% = 80%.
The mistake that loses marks
A common slip is to invert the ratio and write Vₛ = 240 × (1200 ÷ 60) = 4800 V. That answer is larger than the input, but the transformer has fewer secondary turns.
The sense check catches it. A step-down transformer must give a smaller voltage, so the ratio must be smaller than one.
Check yourself
A transformer takes 12 V on a primary with 50 turns and must give 240 V. How many secondary turns are needed, and is it step-up or step-down?
Answer
Nₛ = Nₚ × (Vₛ ÷ Vₚ) = 50 × (240 ÷ 12) = 50 × 20 = 1000 turns.
The output voltage is larger than the input, so it is a step-up transformer.
What to study next
To see transformers at work in the power grid, go to explaining transmission losses. Then test the calculations in the practice set.
The units and significant figure checker helps check your answers. For a teacher to go through transformer problems with you, see online one-to-one Physics tuition or the one-hour trial class (from RM50).