⚡ Transformers

Step-up and step-down · Turns ratio equation · Power conservation · National Grid efficiency

AQA GCSE Physics 4.7 | Year 11 Higher

🔁 Explain how a transformer works using electromagnetic induction

📐 Apply the turns ratio equation: V₁/V₂ = n₁/n₂

⬆️ Distinguish between step-up and step-down transformers

⚡ Use the power conservation equation: V₁I₁ = V₂I₂

🔌 Explain why the National Grid transmits electricity at high voltage

📊 Calculate efficiency losses and energy wasted in transmission

🔁 How Transformers Work

A transformer is a device that changes the size of an alternating voltage. It consists of two coils of wire — the primary coil and the secondary coil — wound around a shared iron core.

Electromagnetic Induction in Transformers: When an alternating current (a.c.) flows through the primary coil, it creates a constantly changing magnetic field in the iron core. This changing magnetic field passes through the secondary coil and induces an alternating voltage across it. This process is called mutual induction.

Key points about transformer operation:

Transformers only work with alternating current (a.c.) — a steady direct current (d.c.) produces a constant magnetic field that does not change, so no voltage is induced in the secondary coil.
The iron core is laminated (made of thin sheets separated by insulation) to reduce energy losses caused by eddy currents circulating within the core.
The frequency of the output a.c. is the same as the input — in the UK, mains electricity is 50 Hz.

A transformer does NOT work with d.c. The changing magnetic flux is essential for inducing a voltage.

📐 The Turns Ratio Equation

The ratio of the voltages across the two coils depends on the ratio of the number of turns on each coil. This is expressed by the turns ratio equation:

V₁ / V₂ = n₁ / n₂

Symbol	Quantity	Unit
V₁	Primary (input) voltage	Volts (V)
V₂	Secondary (output) voltage	Volts (V)
n₁	Number of turns on primary coil	No unit (turns)
n₂	Number of turns on secondary coil	No unit (turns)

This equation can be rearranged to find any unknown quantity:

V₂ = V₁ × (n₂ / n₁)

Step-up transformer: n₂ > n₁, so V₂ > V₁. The output voltage is greater than the input voltage. The output current is smaller than the input current.

Step-down transformer: n₂ < n₁, so V₂ < V₁. The output voltage is less than the input voltage. The output current is greater than the input current.

For example, if a step-up transformer has 100 turns on the primary and 1000 turns on the secondary, the turns ratio is 1:10, and the output voltage is 10 times the input voltage.

⚡ Power Conservation in Transformers

An ideal (100% efficient) transformer conserves energy — the power input equals the power output. Since power P = V × I, we can write:

V₁ × I₁ = V₂ × I₂

Symbol	Quantity	Unit
V₁	Primary voltage	Volts (V)
I₁	Primary current	Amperes (A)
V₂	Secondary voltage	Volts (V)
I₂	Secondary current	Amperes (A)

This equation reveals a crucial trade-off: when voltage increases, current must decrease proportionally, and vice versa. You cannot get more power out than you put in.

A step-up transformer increases voltage but decreases current by the same factor. A step-down transformer decreases voltage but increases current by the same factor.

In real transformers, small amounts of energy are lost due to:

Resistance heating in the copper coil wires (P = I²R losses)
Eddy currents in the iron core (reduced by lamination)
Magnetisation losses (hysteresis) as the core is repeatedly magnetised and demagnetised

However, modern power transformers can achieve efficiencies of 98–99%, making them among the most efficient electrical devices. For GCSE calculations, unless stated otherwise, you assume transformers are 100% efficient.

🔌 The National Grid and Transmission Efficiency

The National Grid is the network of cables and transformers that carries electricity from power stations to homes, schools, and factories across the UK. It operates at very high voltages — up to 400,000 V (400 kV).

Why transmit at high voltage?

The cables in the National Grid have resistance. When current flows through them, energy is wasted as heat according to:

Power wasted = I² × R

If the transmission current is halved (by doubling the voltage), the power wasted is reduced by a factor of four (since it depends on I²). This is a huge saving over long distances.

Transmitting at HIGH voltage means LOW current, which means much LESS energy wasted as heat in the cables (P = I²R).

How it works in practice:

Power stations generate electricity at around 25,000 V (25 kV)
A step-up transformer increases this to 132,000–400,000 V for long-distance transmission
Near homes and businesses, step-down transformers reduce the voltage in stages — first to 33 kV or 11 kV for industry, then to 230 V for domestic use

The efficiency of the National Grid can be calculated using:

Efficiency = (useful power output / total power input) × 100%

Power loss in cables: P_loss = I² × R, where R is the total resistance of the transmission cables and I is the transmission current.

📊 Summary: Key Equations

Turns ratio: V₁ / V₂ = n₁ / n₂

Power conservation: V₁ × I₁ = V₂ × I₂

Power loss in cables: P = I² × R

Efficiency (%): η = (P_out / P_in) × 100

All four equations above may be needed in a single exam question — practise combining them!

Example 1: A transformer has 500 turns on the primary coil and 2000 turns on the secondary coil. The primary voltage is 230 V. Calculate the secondary (output) voltage and state whether it is step-up or step-down.

1 Write down the turns ratio equation: V₁ / V₂ = n₁ / n₂

2 Identify values: V₁ = 230 V, n₁ = 500, n₂ = 2000, V₂ = ?

3 Rearrange for V₂: V₂ = V₁ × (n₂ / n₁)

4 Substitute: V₂ = 230 × (2000 / 500) = 230 × 4 = 920 V

5 Since n₂ > n₁ (2000 > 500), the output voltage is higher than the input — this is a step-up transformer.

✅ Output voltage V₂ = 920 V. This is a step-up transformer (turns ratio 1:4).

Example 2: A step-up transformer increases the voltage from 25,000 V to 400,000 V for National Grid transmission. The primary current is 800 A. Assuming the transformer is 100% efficient, calculate the transmission current in the secondary coil.

1 Write down the power conservation equation: V₁ × I₁ = V₂ × I₂

2 Identify values: V₁ = 25,000 V, I₁ = 800 A, V₂ = 400,000 V, I₂ = ?

3 Rearrange for I₂: I₂ = (V₁ × I₁) / V₂

4 Substitute: I₂ = (25,000 × 800) / 400,000

5 Calculate numerator: 25,000 × 800 = 20,000,000 W (20 MW)

6 I₂ = 20,000,000 / 400,000 = 50 A

✅ Transmission current I₂ = 50 A. Voltage increased by factor 16, current decreased by factor 16.

Example 3: Electricity is transmitted along cables with a total resistance of 4 Ω at a current of 50 A. (a) Calculate the power wasted in the cables. (b) If the same power were transmitted at 10× the current (500 A), what would the power loss be? Compare the two.

1 Part (a): Use P_loss = I² × R with I = 50 A, R = 4 Ω

2 P_loss = 50² × 4 = 2500 × 4 = 10,000 W = 10 kW

3 Part (b): Use P_loss = I² × R with I = 500 A, R = 4 Ω

4 P_loss = 500² × 4 = 250,000 × 4 = 1,000,000 W = 1000 kW

5 Comparison: 1000 kW ÷ 10 kW = 100 times more power wasted when current is 10× larger. Current increased by ×10 → power loss increased by ×10² = ×100 (because P ∝ I²).

✅ (a) Power loss = 10 kW at 50 A. (b) Power loss = 1000 kW at 500 A — 100× more energy wasted. This demonstrates why high-voltage (low-current) transmission is essential.

Example 4: A transformer steps voltage down from 11,000 V to 230 V. The secondary coil carries a current of 40 A. (a) Calculate the primary current. (b) Calculate the number of turns on the primary coil if there are 460 turns on the secondary coil.

1 Part (a): Use power conservation V₁ × I₁ = V₂ × I₂

2 Values: V₁ = 11,000 V, V₂ = 230 V, I₂ = 40 A, I₁ = ?

3 Rearrange: I₁ = (V₂ × I₂) / V₁ = (230 × 40) / 11,000

4 I₁ = 9,200 / 11,000 = 0.836 A (≈ 0.84 A)

5 Part (b): Use turns ratio V₁/V₂ = n₁/n₂, so n₁ = n₂ × (V₁/V₂)

6 n₁ = 460 × (11,000 / 230) = 460 × 47.83 = 22,000 turns

✅ (a) Primary current I₁ ≈ 0.84 A. (b) Primary coil has 22,000 turns. (This is a step-down transformer: high turns → high voltage on primary side.)

Question 1: A transformer has 200 turns on the primary coil and 50 turns on the secondary coil. What type of transformer is this, and what happens to the voltage?

Question 2: A transformer steps voltage from 230 V up to 11,500 V. What is the turns ratio n₁ : n₂?

Question 3: A transformer has 1000 turns on the primary and 50 turns on the secondary. The primary voltage is 240 V. Calculate the secondary voltage in volts.

Question 4: A 100% efficient transformer has a primary voltage of 400 V and primary current of 5 A. The secondary voltage is 20 V. Calculate the secondary current in amperes.

Question 5: Electricity is transmitted at 200,000 V instead of 10,000 V along the same cables (resistance = 2 Ω). By what factor is the power loss reduced?

Challenge 1 (6 marks): A power station generates electricity at 25 kV with a power output of 500 MW. A step-up transformer increases the voltage to 400 kV for National Grid transmission. The transmission cables have a total resistance of 5 Ω.

(a) Calculate the transmission current in the cables.

(b) Calculate the power wasted as heat in the cables.

(c) Calculate the efficiency of the transmission.

Challenge 2 (5 marks): A student claims: "Using a step-up transformer before transmission means you get more power for free — the voltage is bigger so the power must be bigger." Evaluate this claim using your knowledge of transformers and conservation of energy. Include relevant equations in your answer.

Challenge 3 (6 marks): The National Grid delivers 50 MW of power to a region. The transmission cables have resistance 8 Ω. Compare the power lost if electricity is transmitted at (a) 100,000 V and (b) 500,000 V. Show all working and explain which is more efficient.

Challenge 4 (4 marks): A transformer has 3000 turns on the primary coil. It steps voltage from 6000 V down to 120 V. The secondary coil carries 25 A. Calculate: (a) the number of turns on the secondary coil, and (b) the power input to the primary coil, assuming 100% efficiency.