Electromagnetic Induction
Magnetism & Electromagnetism
Voltage-and-turns ratio
For an ideal transformer, the voltage on each side of the iron core is proportional to the number of turns on that side:
Vp / Vs = Np / Ns
- where:
- Vp = voltage across the primary coil (V)
- Vs = voltage across the secondary coil (V)
- Np = number of turns on the primary coil
- Ns = number of turns on the secondary coil
- The equation can equally be written upside down (Vs / Vp = Ns / Np). Pick the form that puts the unknown on the top of a fraction so you have less rearranging to do
- The key fact: the ratio of voltages equals the ratio of turns
Common exam question
Stating the transformer equation and finding the turns
Question: State the formula linking input voltage, output voltage and turns ratio, then calculate the turns on the secondary coil (1 mark, then 3 marks).
The formula mark takes Vp/Vs = Np/Ns in any rearrangement or in words; input/output for primary/secondary, T or n for turns, even "coils" for "turns", are allowed, but the words "turns ratio" in place of the two turn numbers are rejected. Asked in 3 of the 24 papers, all on Paper 2.
The calculation gives one mark each for substitution, rearrangement and evaluation; a bare correct answer earns all three. A power-of-ten slip (kV) loses a mark, and the answer needs at least 2 significant figures, rounded not truncated: a truncated whole number lost the final mark in one paper. One paper also asked how to change the primary coil to raise the output voltage: fewer turns on the primary; answers about the secondary, or about raising the primary's current, power or voltage, are ignored.
Worked example
Transformer equation: finding the number of turns
A step-up transformer has a primary voltage of 25 V and 200 turns on the primary coil. The secondary voltage is 100 V. Calculate how many turns the secondary coil must have.
Solution:
- Write the transformer equation: Vp / Vs = Np / Ns
- Rearrange for Ns: Ns = Np × (Vs / Vp)
- Substitute: Ns = 200 × (100 / 25)
- Ns = 200 × 4 = 800 turns
Conservation of energy
- An ideal transformer is 100 % efficient, with no energy lost as heat in the coils, the core, or eddy currents
- Real transformers reach about 99 % efficiency; the small loss appears as gentle warming of the iron core
- For an ideal transformer, the input electrical power equals the output electrical power:
Vp × Ip = Vs × Is
- where:
- Ip = current in the primary coil (A)
- Is = current in the secondary coil (A)
- This is just the statement P = V × I applied to both sides of the transformer
- A direct consequence: if the voltage is stepped up by some factor n, the current is stepped down by the same factor n, and vice versa
Common exam question
Using input power = output power on a charger label
Question: From a charger label giving input and output voltages and currents, explain how it shows a step-down transformer, show it is approximately 100 % efficient, or calculate the input current assuming 100 % efficiency (2–3 marks).
Step-down from the label is two marks: the output voltage is lower than the input voltage, and the output current is higher than the input current. Set in 2 of the 24 papers, both on Paper 2.
Showing it is about 100 % efficient is three marks: any attempt at a power (voltage × current), one power correct, and a statement that the two powers are about equal, or an efficiency worked out as about 100 %. For the input current, find the output power first (output voltage × output current), equate the input power to it and divide by the input voltage; substitution, rearrangement and evaluation earn one mark each, with ECF from a wrong output power.
Worked example
Input current of a step-down transformer
A step-down transformer in a garden-light supply takes 230 V from the mains and delivers 12 V at 2.5 A to the lamps. Assuming the transformer is 100 % efficient, calculate the current in the primary coil.
Solution:
- Output power = Vs × Is = 12 × 2.5 = 30 W
- For 100 % efficiency, input power = output power, so Vp × Ip = 30 W
- Ip = 30 ÷ 230 = 0.1304… A
- Input current = 0.13 A
The high-voltage side carries the smaller current: if a step-down transformer's input current comes out larger than its output current, the division is the wrong way round.