A transformer is connected to a 250 V a.c. supply. The primary coil has 5000 turns and the secondary voltage…

Analyze the question

We have an ideal transformer with:

• Primary voltage, Vp = 250 V
• Primary turns, Np = 5000
• Secondary voltage, Vs = 10 V
• Secondary turns, Ns = ?

Concept

For a transformer, the voltage ratio equals the turns ratio:

Vs / Vp = Ns / Np

This is a step-down transformer because the secondary voltage is lower than the primary voltage, so the secondary must have fewer turns.

Solution

Ns = Np × (Vs / Vp)

Ns = 5000 × (10 / 250)

Ns = 5000 × 0.04

Ns = 200 turns

Answer

The secondary coil has 200 turns.

Tip

For transformer questions, write down Vs/Vp = Ns/Np first. Then check that your answer makes sense: a step-down transformer (lower voltage out) must have fewer secondary turns than primary turns. Here the ratio is 250 : 10 = 25 : 1, so 5000 ÷ 25 = 200. Dividing by the ratio is a quick shortcut.