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1.9.7Electricity, Energy and Waves

Transformer Calculations

5 min read 5 parts Lesson 53 of 54 Unit quiz

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Section 1 of 5The Turns Ratio Equation

1.9.7 Transformer Calculations

The voltages across the coils are in the same ratio as the numbers of turns on them.

Equation
  • Vp ÷ Vs = Np ÷ Ns, where V is the voltage across a coil and N is its number of turns.
Subscripts
  • The letter p stands for the primary coil, which is the input, and s stands for the secondary coil, the output.
Rearranging
  • Vs = Vp × Ns ÷ Np and Ns = Np × Vs ÷ Vp are the forms used most often in calculations.
Voltage units
  • The units can be volts or kilovolts as long as both voltages use the same unit.

Section 2 of 5Power and Current

An ideal transformer has no energy loss, so power in equals power out.

Power and Current
Power equation
  • Vp × Ip = Vs × Is, because power is voltage multiplied by current in each coil.
Step-up
  • If the voltage is increased, the current in the secondary coil is smaller by the same factor.
Step-down
  • If the voltage is decreased, the secondary current is larger by the same factor.
Real transformers
  • Heat in the coils and core means the output power is slightly less than the input power.

Section 3 of 5Strategy for Calculations

1
Write down the known values and label each one as primary or secondary before any substitution.
2
Choose the turns ratio equation when turns are involved, or the power equation when currents are involved.
3
Rearrange the equation to make the unknown the subject before putting numbers in.
4
Substitute the values, calculate, and round to a sensible number of significant figures.
5
Check that the answer makes sense: a step-down transformer must give a smaller voltage and a larger current.

Section 4 of 5Worked Example

Question

  • A transformer has 250 turns on its primary coil and 50 turns on its secondary coil.
  • The primary is connected to a 230 V supply.
  • (a) Calculate the secondary voltage.
  • (b) The secondary current is 2.0 A.
  • Assuming the transformer is 100% efficient, calculate the primary current.

  1. (a) Rearrange the turns ratio: Vs = Vp × Ns ÷ Np.
  2. SubstituteVs = 230 × 50 ÷ 250 = 46 V.
  3. (b) Output power: Vs × Is = 46 × 2.0 = 92 W.
  4. Input power equals output power, so Ip = 92 ÷ 230 = 0.40 A.

Answer

  • (a) 46 V, a step-down transformer;
    • (b) 0.40 A

Section 5 of 5Exam Checklist & Tips

1.9.7 – Key Points for the Exam

  • Turns ratio The ratio of the number of turns on the primary coil to the number on the secondary coil.
  • Efficiency The fraction of the input energy that is transferred as useful output energy.
  • Step-down A transformer that reduces the voltage.
  • Power The rate of energy transfer, found from voltage multiplied by current.

Common Mistakes

  • Putting the secondary values on the top of the equation and the primary values on the bottom without adjusting.
  • Forgetting to use the power equation for currents and trying to use the turns ratio for them directly.
  • Expecting a step-up transformer to give more power; the ideal power stays the same.
  • Mixing units, for example volts with kilovolts, in the same equation.
Transformer Golden Equations Physics Standard

Transformer Turns Ratio & Efficiency

Ratio: Vp / Vs = Np / Ns = Is / Ip

  • Step-up reduces grid thermal loss (P = I2R).
  • Laminated core prevents eddy currents.