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15.8 Transformers in Action

GCSE Physics · AQA · Chapter 15: Electromagnetism

A free GCSE Physics lesson for AQA (8463) from OBA School: higher tier, physics only. The turns-ratio equation, power in a 100% efficient transformer, efficiency and the National Grid. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • (Higher tier) use Vp ÷ Vs = np ÷ ns to calculate a p.d. or a number of turns
  • (Higher tier) state whether ns is bigger or smaller than np for step-up and step-down transformers
  • (Higher tier) use Vp × Ip = Vs × Is for a 100% efficient transformer, for example to find the current drawn from the supply
  • (Higher tier) calculate the efficiency of a real transformer
  • (Higher tier) explain why the National Grid transmits electrical power at a very high p.d.

Key words

  • Turns ratio: np ÷ ns: the number of turns on the primary divided by the number on the secondary. It equals Vp ÷ Vs.
  • Vp, Vs: The p.d.s across the primary and secondary coils, in volts.
  • Ip, Is: The currents in the primary and secondary coils, in amperes.
  • 100% efficient: All the power supplied to the primary coil is delivered by the secondary coil: Vp Ip = Vs Is.
  • National Grid: The network of cables and transformers that connects power stations to consumers across the country.

The transformer equation

Vp ÷ Vs = np ÷ ns

Vp, Vs in volts (V); np, ns are numbers of turns (no unit)

Rearranged: Vs = Vp × ns ÷ np ns = np × Vs ÷ Vp

Step-up: ns > np, so Vs > Vp. Step-down: ns < np, so Vs < Vp.

Worked example: finding the number of turns

A step-down transformer changes 230 V to 9.2 V. Its primary has 1500 turns. How many turns are on the secondary?
ns = np × Vs ÷ Vp = 1500 × 9.2 ÷ 230

Answer: ns = 60 turns

Worked example: finding the output p.d.

A local substation transformer has 4400 turns on its primary and 92 turns on its secondary. The primary p.d. is 11 000 V.
Vs = Vp × ns ÷ np = 11 000 × 92 ÷ 4400

Answer: Vs = 230 V

Exam tip: Check your answer makes sense: a step-down transformer must give an output smaller than its input, and the coil with more turns always has the bigger p.d.

Power and current: Vp × Ip = Vs × Is

Good transformers are very nearly 100% efficient. If we assume 100% efficiency, the power in equals the power out. Since power = p.d. × current (P = V I):

Vp × Ip = Vs × Is (100% efficient transformer)

Ip = Vs × Is ÷ Vp Is = Vp × Ip ÷ Vs

Stepping the p.d. up steps the current down by the same factor, and the other way round.

Worked example: current drawn from the mains

A transformer steps 230 V mains down to 12 V for a lamp that takes 4.0 A. Assume 100% efficiency. Find the primary current.
Ip = Vs × Is ÷ Vp = 12 × 4.0 ÷ 230 = 48 ÷ 230 = 0.2087 A

Answer: Ip = 0.21 A (2 s.f.)

Real transformers waste a little energy, for example by heating the coils and the core. Then the output power is less than the input power:

efficiency = useful output power ÷ total input power (× 100 for a percentage)

Worked example: efficiency of a charger transformer

Input: 230 V, 1.5 A. Output: 24 V, 13.0 A.
input power = 230 × 1.5 = 345 W; output power = 24 × 13.0 = 312 W
efficiency = 312 ÷ 345 = 0.904

Answer: 90%

Why the National Grid uses a high p.d.

  • For a given power, P = V I. Raising the p.d. lowers the current needed.
  • The power wasted heating the cables is P = I² R. It depends on the square of the current, so a 10 times smaller current wastes 100 times less power.
  • So step-up transformers raise the p.d. (and lower the current) before transmission. This makes the grid much more efficient and allows thinner, cheaper cables.
  • Step-down transformers then lower the p.d. to 230 V, which is safer to use in homes.

Worked example: comparing power losses

500 kW is sent through cables of total resistance 8.0 Ω, first at 10 kV, then at 100 kV.
At 10 kV: I = P ÷ V = 500 000 ÷ 10 000 = 50 A; loss = I² R = 50² × 8.0 = 20 000 W
At 100 kV: I = 500 000 ÷ 100 000 = 5.0 A; loss = 5.0² × 8.0 = 200 W

Answer: 10 times the p.d. → 100 times less power wasted

Common mistakes

  • Turning the ratio upside down. Keep primary with primary: Vp ÷ Vs = np ÷ ns.
  • Thinking a step-up transformer increases the power. It increases the p.d. but decreases the current; the power cannot increase.
  • Using Vp × Ip = Vs × Is for a transformer that is not 100% efficient without saying so.
  • Saying high p.d. reduces resistance. The resistance of the cables is the same; the current is smaller, so less power is wasted.
  • Forgetting to convert kV to V or kW to W.

Revision questions

Try these, then check your answers below each one.

Question 1. (Higher tier) A transformer steps 230 V down to 46 V. Its primary coil has 1000 turns. Calculate the number of turns on the secondary.

Answer: 200 turns

Working: ns = np × Vs ÷ Vp = 1000 × 46 ÷ 230 = 200 turns.

Question 2. (Higher tier) A transformer has 200 turns on its primary and 3000 turns on its secondary. The primary p.d. is 12 V. Calculate the secondary p.d.

Answer: 180 V

Working: Vs = 12 × 3000 ÷ 200 = 180 V (step-up).

Question 3. (Higher tier) A 100% efficient transformer is connected to the 230 V mains. Its output is 23 V and the current in the secondary is 5.0 A. Calculate the current in the primary coil.

Answer: 0.5 A

Working: Ip = Vs × Is ÷ Vp = 23 × 5.0 ÷ 230 = 0.50 A.

Related lessons

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