Transformers

How transformers step voltage up or down using electromagnetic induction, and why the National Grid uses them.

Spec Points Covered
  • Describe the construction of a transformer and explain how it works using Faraday's law.
  • Apply the transformer equation Vs/$Vp = Ns/Np$ to step-up and step-down transformers.
  • Apply powerThe rate of energy transfer. Measured in watts (W). conservation ($VpIp = VsIs)$ to calculate secondary currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). in an ideal transformer.
  • Calculate transformer efficiencyThe ratio of useful energyThe capacity to do work. Measured in joules (J). output to total energyThe capacity to do work. Measured in joules (J). input, expressed as a fraction or percentage. using $EfficiencyThe ratio of useful energyThe capacity to do work. Measured in joules (J). output to total energy input, expressed as a fraction or percentage. = (VsIs)/(VpIp) x 100%$.
  • Explain the causes of energy loss in a real transformer and how each is reduced.
  • Explain why the National Grid transmits at high voltageThe energy transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. and calculate powerThe rate of energy transfer. Measured in watts (W). losses using $P = I^{2} R$.
Notes
01 A transformer uses changing flux to transfer electrical energy between two coils Transformer 3.7.5.6 → 02 The turns ratio determines whether voltage goes up or down $\frac{V_s}{V_p} = \frac{N_s}{N_p}$ 3.7.5.6 → 03 A transformer trades voltage for current while conserving power $V_p I_p = V_s I_s$ 3.7.5.6 → 04 Real transformers waste energy, and efficiency tells you how much $\text{Efficiency} = \frac{V_s I_s}{V_p I_p} \times 100\%$ 3.7.5.6 → 05 Every transformer loss has a specific engineering fix 3.7.5.6 → 06 The National Grid transmits at high voltage because P_loss = I²R 3.7.5.6 → 07 Transformer calculations always come back to three equations 3.7.5.6 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Transformer equation
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
  • Where:
    • $V_s$ = secondary (output) voltage (V)
    • $V_p$ = primary (input) voltage (V)
    • $N_s$ = number of turns on secondary coil
    • $N_p$ = number of turns on primary coil
Assumes ideal transformer. Step-up: Ns > Np. Step-down: Ns < Np.
Power conservation (ideal transformer)
$$V_p I_p = V_s I_s$$
  • Where:
    • $V_p$ = primary voltage (V)
    • $I_p$ = primary current (A)
    • $V_s$ = secondary voltage (V)
    • $I_s$ = secondary current (A)
Only valid for an ideal (100% efficient) transformer. If voltage increases, current decreases by the same factor.
Power loss in transmission cables
$$P_{\text{loss}} = I^2 R$$
  • Where:
    • $P_loss$ = power dissipated in cables (W)
    • $I$ = current in cables (A)
    • $R$ = total resistance of cables (ohm)
Combined with P = IV to give P_loss = P²R/V², showing losses are proportional to 1/V². This is why the National Grid uses high voltage.
Transformer efficiency
$$\text{Efficiency} = \frac{V_s I_s}{V_p I_p} \times 100\%$$
  • Where:
    • $V_s I_s$ = output power (W)
    • $V_p I_p$ = input power (W)
Always less than 100% for real transformers. Rearrange to find output: VsIs = (efficiency/100) x VpIp.
Transmission loss in terms of voltage
$$P_{\text{loss}} = \frac{P^2 R}{V^2}$$
  • Where:
    • $P_loss$ = power dissipated in cables (W)
    • $P$ = power being transmitted (W)
    • $R$ = total resistance of cables (ohm)
    • $V$ = transmission voltage (V)
Derived from P_loss = I²R and I = P/V. Shows that doubling the transmission voltage quarters the power loss.
Q Retrieval Practice All 10 Questions →
Q1. Describe the basic structure of a transformer.
  • A transformer consists of a primary coil and a secondary coil, both wound on a shared soft iron core.
  • The coils are electrically isolated from each other.
Q2. Explain why a transformer only works with AC and not DC.
  • AC produces a continuously changing currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A)., which creates a continuously changing magnetic fluxThe product of magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³. and the area perpendicular to the field. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area. (Wb). in the core.
  • This changing flux induces an EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). in the secondary coil (Faraday's lawThe magnitude of the induced EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). is proportional to the rate of change of magnetic flux linkageThe product of magnetic flux and the number of turns of a coil. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area.-turns (Wb turns)..).
  • DC produces a constant currentThe rate of flow of charge. Measured in amperes (A)., so the flux is constant and no EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). is induced.
Q3. State the transformer equation and define each term.
Vs/Vp = Ns/Np, where Vs = secondary voltageThe energy transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference., Vp = primary voltageThe energy transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference., Ns = number of turns on the secondary coil, Np = number of turns on the primary coil.
Q4. What is the difference between a step-up and a step-down transformer?
  • A step-up transformer has more turns on the secondary than the primary (Ns > Np), so the output voltage is greater than the input voltage.
  • A step-down transformer has fewer turns on the secondary (Ns < Np), so the output voltage is less than the input.
Q5. State the powerThe rate of energy transfer. Measured in watts (W). conservation equation for an ideal transformer.
  • VpIp = VsIs.
  • Input power equals output power.
  • If voltage is stepped up, current is stepped down by the same factor.