Extended · Practice questions · Transformer equations

Power, current, loss.

Six original Cambridge-style questions on the transformer power equation: power conservation, finding the secondary current, the I-squared-R cable loss, and why the grid uses high voltage.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

What the examiner wants

Conserve power, then watch the squared term.

Power: VₚIₚ = VₛIₛ for an ideal transformer.
Current: rearrange to find the missing current.
Loss: power wasted in a cable is I²R; a small current means a tiny loss.

Recall

[2 marks]

Write the equation linking the voltages and currents of an ideal (100% efficient) transformer, and state what it tells you about the power.

Vₚ × Iₚ = Vₛ × Iₛ

The power put into the primary equals the power taken from the secondary. ✓✓

Calculation

[3 marks]

A transformer steps 230 V up to 1150 V. The primary current is 5.0 A. Calculate the secondary current, assuming the transformer is 100% efficient.

Iₛ = VₚIₚ ÷ Vₛ = (230 × 5.0) ÷ 1150

Iₛ = 1.0 A

voltage up 5 times, so current down 5 times

Calculation

[2 marks]

A current of 8.0 A flows in a transmission cable of resistance 3.0 Ω. Calculate the power wasted as heat in the cable.

P = I²R = 8.0² × 3.0 = 64 × 3.0

P = 192 W

Analysis

[2 marks]

In a transmission cable the current is reduced to half its original value. State what happens to the power wasted in the cable, and explain.

The power wasted falls to one quarter. ✓
The loss is I²R, and halving the current gives (1/2)² = 1/4 of the loss. ✓

Application

[3 marks]

Explain why electrical power is sent through the grid at a very high voltage rather than a low one. Refer to the current and the power lost in the cables.

For a fixed power, a higher voltage means a smaller current. ✓
The power wasted heating the cables is I²R. ✓
A smaller current wastes much less energy, so transmission is more efficient. ✓

Calculation

[4 marks]

A power of 20 kW is sent along a cable of resistance 2.0 Ω. Calculate the power wasted in the cable when it is sent at 200 V, and again when it is sent at 20 000 V. Comment on the difference.

At 200 V:

I = P ÷ V = 20000 ÷ 200 = 100 A, loss = 100² × 2.0 = 20 000 W

At 20 000 V:

I = 20000 ÷ 20000 = 1.0 A, loss = 1.0² × 2.0 = 2.0 W

The low-voltage cable wastes almost all the power; the high-voltage cable wastes almost none. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.