The Transformer: MDCAT Physics notes
The Transformer MDCAT notes: mutual induction, turns ratio Vs/Vp = Ns/Np, step-up and step-down, ideal power balance, eddy current losses and transmission.
Construction and principle
A transformer consists of two coils of insulated copper wire, the primary and the secondary, wound on the same laminated soft iron core. There is no electrical connection between the coils; they are linked magnetically by the flux in the core.
It works on the principle of mutual induction (electromagnetic induction, Faraday's law). An alternating current in the primary sets up an alternating flux in the core, and this changing flux induces an alternating emf in the secondary.
A transformer changes (steps up or steps down) an AC voltage. It cannot work on DC: a steady primary current gives a steady flux, so no emf is induced in the secondary.
Turns ratio
The same flux links every turn of both coils, so the emf per turn is the same:
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
The output voltage depends on the turns ratio, not on the supply frequency.
Ideal transformer
An ideal transformer has no losses, so power input equals power output:
$$V_pI_p = V_sI_s \quad\Rightarrow\quad \frac{I_s}{I_p} = \frac{V_p}{V_s} = \frac{N_p}{N_s}$$
Current changes in the inverse ratio to voltage.
| Type | Turns | Voltage | Current |
|---|---|---|---|
| Step-up | $N_s > N_p$ | $V_s > V_p$ | $I_s < I_p$ |
| Step-down | $N_s < N_p$ | $V_s < V_p$ | $I_s > I_p$ |
Example: a transformer on a 240 V line delivers 2 A at 4800 V. Assuming 100% efficiency, $I_p = 4800\times2/240 = 40$ A.
If the primary voltage doubles with the same turns ratio and load, the secondary voltage doubles and so the secondary current doubles as well.
Real transformers and losses
In a practical transformer power output is less than power input. Efficiencies are high, typically above 90%.
- Eddy currents: induced currents circulating in closed loops in the core heat it. Reduced by laminating the core.
- Hysteresis loss: repeated magnetisation of the core; reduced by using soft iron.
- Copper loss: $I^2R$ heating in the windings; reduced by using thick wire.
- Flux leakage: not all primary flux reaches the secondary.
Power transmission
Power lost in transmission lines is $I^2R$. At a grid station the voltage is stepped up so the current is small, reducing losses. Near consumers it is stepped down again.
Key formulas
- $V_s/V_p = N_s/N_p$
- $V_pI_p = V_sI_s$ (ideal)
- Efficiency $= P_{\text{out}}/P_{\text{in}}\times100\%$
- Line loss $= I^2R$
Common MDCAT traps
- Coils are linked magnetically, not electrically.
- DC in the primary gives no secondary emf.
- Step-down transformer gives a larger secondary current.
- Stepping up voltage by 10 times cuts the current to one-tenth.
- Transmission loss is reduced by increasing voltage, not current.
Quick revision
- Transformer works on mutual induction.
- Core is laminated soft iron.
- Step-up has more secondary turns.
- In an ideal transformer input power equals output power.
- Secondary voltage is inversely proportional to secondary current at fixed power.