Egypt Secondary 3 Physics, Week 10: The transformer: voltage and current ratios

The sine wave, the DC generator and the transformer

Week 10 · Chapter 3 (C): the sine wave of a generator and its frequency (50 Hz at home), the effective value (0.707 of the maximum), rectification and the DC generator (split-ring commutator), the transformer (turns, voltage and current ratios, step-up and step-down) · 3 lessons

The transformer: voltage and current ratios

Physics Sec 3 Term 1, Chapter 3: pp. 73–79

GoalUse Vs ÷ Vp = Ns ÷ Np and Ip ÷ Is = Ns ÷ Np for an ideal transformer and tell step-up from step-down.

New words

transformer · two coils (primary and secondary) wound on a laminated soft-iron core; it changes an AC voltage by mutual inductionstep-up and step-down · step-up: Ns > Np, so Vs > Vp; step-down: Ns < Np, so Vs < Vpideal transformer · one with no energy losses, so the power into the primary equals the power out of the secondary: VpIp = VsIs

Explanation

An alternating current in the primary makes a flux that changes all the time. The laminated soft-iron core guides almost all of it through the secondary, where by mutual induction it induces an emf in each turn. Each turn has the same emf, so Vs ÷ Vp = Ns ÷ Np. For an ideal transformer the power is the same on both sides, VpIp = VsIs, so Ip ÷ Is = Ns ÷ Np: a step-up transformer raises the voltage and lowers the current, a step-down transformer does the opposite. The frequency does not change. A transformer works only with alternating current: a steady current makes a steady flux, and a steady flux induces nothing. Real transformers lose a little energy as heat in the wires and the core; here they are ideal. Do not open a charger or any transformer: this is a paper topic.

	Step-up (Ns > Np)	Step-down (Ns < Np)
secondary voltage	larger than Vp	smaller than Vp
secondary current	smaller than Ip	larger than Ip
power (ideal)	the same	the same
frequency	unchanged	unchanged

Worked examples

Np = 400, Ns = 60 and Vp = 220 V. Vs = Vp × Ns ÷ Np = 220 × 60 ÷ 400 = 33 V. If Is = 1.5 A, then Ip = Is × Ns ÷ Np = 1.5 × 60 ÷ 400 = 0.225 A. Check the power: 220 × 0.225 = 49.5 W and 33 × 1.5 = 49.5 W.

A step-up transformer has Np = 50, Ns = 1500 and an AC primary of 12 V. Vs = 12 × 1500 ÷ 50 = 360 V. If Is = 0.2 A, then Ip = 0.2 × 1500 ÷ 50 = 6 A: the voltage is 30 times larger and the current 30 times smaller.

To get 9 V from a 220 V supply with a primary of Np = 1100 turns, Ns = Np × Vs ÷ Vp = 1100 × 9 ÷ 220 = 45 turns. The ratio Ns ÷ Np is small, so it is a step-down transformer.

Class activity

Paper practice. For a transformer with Np = 100 and Ns = 20, fill in a small table with the primary voltages 220 V, 110 V and 55 V and the secondary voltages. Then say whether it is step-up or step-down, and what happens to the current in the secondary compared with the primary.

Practice

A transformer has Np = 2200 and Ns = 110, with Vp = 220 V. Find Vs.

The same ideal transformer delivers Is = 4 A. Find Ip and the power.

A step-up transformer changes 6 V into 120 V and has Np = 40. Find Ns.

Why does a transformer give no steady output when its primary is joined to a steady cell?