The transformer
Section: Electricity & Magnetism | Syllabus: Cambridge IGCSE Physics (0625)
What is a Transformer?
A transformer changes an alternating voltage from one value to a greater or smaller value. It only works with a.c., not d.c.
A transformer has a primary coil and a secondary coil linked by a shared soft iron core
Transformer Construction
- Primary coil: connected to the a.c. input (N_p turns)
- Secondary coil: connected to the output (N_s turns)
- Soft iron core: links the two coils magnetically
Types of Transformer
- Step-up: N_s > N_p, so V_s > V_p (increases voltage)
- Step-down: N_s < N_p, so V_s < V_p (decreases voltage)
How a Transformer Works
Mutual Induction
When the current in a coil is switched on, off, or changed, a voltage is induced in a neighbouring coil. This effect is called mutual induction, and is an example of electromagnetic induction.
Switching the current in coil A on or off induces a current in coil B, even though the coils are not directly connected
- Switching on the current in the primary sets up a magnetic field; as its field lines grow outwards, they cut the secondary coil
- A p.d. is induced in the secondary until the current in the primary reaches its steady value (the field stops changing)
- Switching the current off in the primary makes the field die away; as the collapsing field lines cut the secondary again, a p.d. is again induced, in the opposite direction
- Changing the primary current (e.g. by quickly altering a rheostat) has the same effect, inducing a p.d. in the secondary
An alternating current keeps the field constantly growing and collapsing, so it continuously induces an alternating voltage in the secondary. This is why a transformer only works with a.c.
The Transformer Equation
For a transformer in which all the field lines from the primary cut the secondary, the secondary voltage is given by:
(V_p/V_s) = (N_p/N_s)
where V_p/V_s are the primary/secondary voltages and N_p/N_s are the number of turns on the primary/secondary coils.
Worked Example: Step-Down Transformer
A transformer has 1000 primary turns and 50 secondary turns. If the input voltage is 230 V, what is the output voltage?
- Step 1: write down the equation. (V_p/V_s) = (N_p/N_s)
- Step 2: substitute the values. (230/V_s) = (1000/50)
- Step 3: calculate the answer. V_s = (230 × 50/1000) = 11.5 V
Power and Efficiency
If we assume all the electrical energy given to the primary appears in the secondary (i.e. energy is conserved), the transformer is 100% efficient (an "ideal" transformer). Then power in primary = power in secondary:
I_p V_p = I_s V_s
- If voltage increases (step-up), current decreases in the same ratio
- If voltage decreases (step-down), current increases in the same ratio
Worked Example: Current in a Transformer
A 100% efficient transformer steps up 12 V to 240 V. If the primary current is 10 A, what is the secondary current?
- Step 1: write down the equation. I_p V_p = I_s V_s
- Step 2: substitute the values. 10 × 12 = I_s × 240
- Step 3: calculate the answer. I_s = (120/240) = 0.5 A
Energy Losses in a Real Transformer
In practice, transformers are not perfectly 100% efficient because of small energy losses:
- Resistance of windings: the copper wire coils have some resistance, so current flowing through them produces heat
- Eddy currents: the iron core sits in the changing magnetic field of the primary, which induces swirling currents (eddy currents) in the core itself, causing heating
These losses are reduced by using a laminated core: thin sheets of iron insulated from one another, which have a high resistance to eddy currents.
High-Voltage Transmission
Transformers are essential for efficient electricity transmission. Power cables have resistance, so electrical energy is transferred to (wasted as) thermal energy during transmission.
Why Transmit at High Voltage?
The power lost as heat in a cable of resistance R is:
P_loss = I^2 R
To transmit the same power P at a higher voltage, the current I = P/V is lower, and since power loss depends on I^2, even a small reduction in current gives a much bigger reduction in power loss.
Worked Example: Power Loss Comparison
A power station transmits 100 kW. Compare the power loss when transmitting at 10 kV versus 100 kV (cable resistance = 10 Ω).
- At 10 kV: I = (P/V) = (100000/10000) = 10 A P_loss = I^2R = 10^2 × 10 = 1000 W
- At 100 kV: I = (P/V) = (100000/100000) = 1 A P_loss = I^2R = 1^2 × 10 = 10 W
- A 10× higher voltage gives 100× less power loss
The National Grid
The National Grid is a network of cables, mostly supported on pylons, connecting all the power stations in a country to consumers. Transformers step the voltage up and down in stages between the power station and the home:
- Power station: generates electricity at around 25 kV
- Step-up transformer: increases this to a very high voltage (e.g. 275 kV to 400 kV) for the Supergrid transmission lines
- Step-down transformers: reduce the voltage in stages (e.g. to 132 kV for regional distribution, then to 33 kV or 11 kV for industry)
- Local step-down transformer: reduces the voltage to 230 V (or 415 V) for homes and villages
Transformers step the voltage up for efficient long-distance transmission, then back down in stages for safe local use
Advantages of High-Voltage Transmission
- Lower power loss in the transmission cables
- Lower currents mean thinner, cheaper cables can be used
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