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4.4.7Electricity and Magnetism

Transformer Calculations — Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 31 of 31

📚 Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Hub / Topical Revision
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Section 1 of 9The transformer equation

Vp / Vs
Np / Ns
  • the ratio of the voltages across the coils equals the ratio of the turns.
    What the symbols mean: V = voltage (V) · N = number of turns · I = current (A) · p = primary coil · s = secondary coil
Symbols
  • Vp and Vs are the primary and secondary voltages (V) and Np and Ns are the numbers of turns.
Flipped
  • Vs / Vp = Ns / Np.
Output voltage
  • Vs = Vp × Ns / Np, so it depends on the turns on both coils and the input voltage.
Layout
  • Layout put the unknown on the top line to minimise rearranging, and use the same letter on top and bottom of each fraction.

Section 2 of 9Step-up and step-down

1Step-up
  • Vs > Vp and Ns > Np.
2Step-down
  • Vs < Vp and Ns < Np.
3Terms
  • Terms the loops of wire are called turns, not coils.

Section 3 of 9Ideal transformer (Extended)

Definition
  • Definition an ideal transformer is 100% efficient.
Conservation of energy
  • Conservation of energy a transformer can raise the voltage but cannot increase the power.
IpVp
IsVs
  • power in the primary equals power in the secondary.
Ratio form
  • Is / Ip = Vp / Vs = Np / Ns.
Check
  • Check the coil with more turns has the larger voltage and the smaller current.

Section 4 of 9Efficiency of real transformers

Efficiency
(power out / power in) × 100%
  • equals IsVs / IpVp × 100%.
Losses
  • Losses real transformers lose energy as heat in the windings and core, so output power is less than input.
Size
  • Size large power transformers can be over 99% efficient, while small ones such as chargers are less efficient.

Section 5 of 9Method for calculations

1
Write down the known quantities with units.
2
Use the turns-ratio equation to find an unknown voltage or number of turns.
3
If a current is needed, use IpVp = IsVs.
4
Check the answer: a step-up transformer gives a higher voltage and a lower current.
  • Units
    • change kilowatts and kilovolts into watts and volts before using the equations.

Section 6 of 9Power loss in transmission (Extended)

1Cable loss
  • P = I2R, so it is proportional to the square of the current.
    What the symbols mean: P = power (W) · I = current (A) · R = resistance (Ω)
2Step-up by a factor of 10
  • Step-up by a factor of 10 the current falls by a factor of 10 and the cable loss falls by a factor of 100.
3Step-down transformers
  • Step-down transformers in substations they reduce the voltage again before the electricity reaches homes.
4Dangerous voltage
  • Dangerous voltage high voltage is too dangerous for homes, so it must be lowered first.

Section 7 of 9More from the specification

1
Transformer stepping and induction motor
  • Transformer stepping and induction motor alternating voltage stepping via electromagnetic induction supplies efficient power distribution to drive industrial electric motor systems.
2
Transformer voltage and turns ratio
  • In an ideal transformer, the ratio of voltages equals the ratio of turns on the primary and secondary coils: Vp / Vs = Np / Ns.
3
Current ratio and electrical power conservation
  • Assuming 100% efficiency, electrical power input equals power output (Vp Ip = Vs Is), yielding Ip / Is = Ns / Np.
4
High-voltage electrical grid transmission
  • Step-up transformers elevate transmission voltages to hundreds of kilovolts,
  • reducing transmission current and minimising I2 R heat losses in national power cables.
5
Electromagnetic induction in solenoids
  • Electromagnetic induction in solenoids moving a permanent magnet into a solenoid cuts magnetic field lines, inducing an electromotive force in the circuit.
6
Lenz's law direction
  • Lenz's law direction induced current flows in an opposite direction such that its magnetic field opposes the change inducing it.
7
Magnetic force on coils
  • Magnetic force on coils alternating magnetic fields generate opposing electromagnetic forces that regulate current through transformer windings.
8
Alternating current
  • Current that continually reverses direction.
9
Induced magnet
  • Material temporarily magnetised in a magnetic field
10
Potential difference
  • Work done by a unit charge passing through a component.
11
Electromagnetic induction
  • Production of an e.m.f. by relative movement of a conductor and a magnetic field.
12
Permanent magnet
  • Magnet whose field is always there.
13
Magnet
  • Object that attracts magnetic materials.
14
Solenoid
  • Long coil of wire carrying a current
15
Conductor
  • Material that allows current to flow.
16
Voltmeter
  • Instrument that measures p.d., connected in parallel.
17
Generator
  • Device that turns kinetic energy into electrical energy.
18
Brushes
  • Carbon contacts pressing on the slip rings.
19
Magnetic field
  • Area around a magnet where its effects can be detected.
20
Field lines
  • Lines showing the direction and strength of a magnetic field.

Section 8 of 9Key terms

TermMeaning
Turns ratioNp / Ns, equal to Vp / Vs.
Ideal transformerTransformer with 100% efficiency.
Efficiency(Power out / power in) × 100%.
PrimaryInput coil.
SecondaryOutput coil.

Section 9 of 9Exam technique

1
Inverting the ratio — the larger voltage belongs to the coil with more turns.
2
Using the voltage ratio for currents without inverting it.
3
Forgetting that efficiency is below 100% for real transformers.
4
Mixing units, such as kilovolts with volts.

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