AcademyAlternating Current
Academy
Transformers
Level 1 - Physics topic page in Alternating Current.
Principle
A transformer uses changing magnetic flux to transfer AC energy between coils. In an ideal transformer, voltage ratio equals turns ratio and input power equals output power.
Notation
\(N_p, N_s\)
primary and secondary turns
\(V_p, V_s\)
primary and secondary rms voltages
\(\mathrm{V}\)
\(I_p, I_s\)
primary and secondary rms currents
\(\mathrm{A}\)
\(P_p, P_s\)
primary and secondary power
\(\mathrm{W}\)
\(\Phi_B\)
magnetic flux through the core
\(\mathrm{Wb}\)
\(\eta\)
efficiency
Method
Derivation 1: Use Faraday's law in both coils
Both coils link the same changing flux in the ideal core, so emf per turn is the same in each coil.
Voltage ratio
\[\frac{V_s}{V_p}=\frac{N_s}{N_p}\]
Derivation 2: Apply ideal power conservation
An ideal transformer has no losses, so input power equals output power.
Power conservation
\[V_pI_p=V_sI_s\]
Current ratio
\[\frac{I_s}{I_p}=\frac{N_p}{N_s}\]
Derivation 3: Include efficiency when needed
Real transformers dissipate some power in windings, cores, and leakage fields. Efficiency compares useful output power with input power.
Efficiency
\[\eta=\frac{P_s}{P_p}\]
Rules
Voltage ratio
\[\frac{V_s}{V_p}=\frac{N_s}{N_p}\]
Ideal power
\[V_pI_p=V_sI_s\]
Current ratio
\[\frac{I_s}{I_p}=\frac{N_p}{N_s}\]
Efficiency
\[\eta=\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}\]
Examples
Question
A transformer has
\[N_p=200\]
\[N_s=1000\]
and \[V_p=24\,\mathrm V\]
Find \(V_s\).Answer
\[V_s=V_p\frac{N_s}{N_p}=24\frac{1000}{200}=120\,\mathrm V\]
Checks
- Transformers require changing flux, so they work with AC, not steady DC.
- A step-up transformer increases voltage and decreases current.
- A step-down transformer decreases voltage and increases current.
- Real transformers have losses, so output power is less than input power.