P7.5 Transformers

What is a transformer?

A transformer is a device that changes the voltage (and current) of an alternating current. It cannot work with direct current. A basic transformer has two coils of wire wound onto an iron core:

• Primary coil: input side (connected to AC supply)
• Secondary coil: output side

The iron core channels the changing magnetic flux from the primary to the secondary. The changing flux induces an EMF in the secondary coil (generator effect).

The turns ratio equation

For an ideal transformer:

V_p / V_s = n_p / n_s

where V = voltage, n = number of turns, subscript p = primary, s = secondary.

• Step-up transformer: n_s > n_p → V_s > V_p (higher output voltage, lower current)
• Step-down transformer: n_s < n_p → V_s < V_p (lower output voltage, higher current)

Power equation for ideal transformer

Since an ideal transformer wastes no energy:

V_p × I_p = V_s × I_s

Power in = Power out. This means when voltage goes up, current goes down proportionally — and vice versa.

Transformers and the National Grid

Power is generated at ~25 kV, stepped up to 400 kV for long-distance transmission. Why? For a given power P = IV, a higher voltage means a lower current. Cable energy loss = I²R — the lower the current, the much smaller the loss (it goes as I squared). At the consumer end, transformers step down the voltage to 230 V for homes, or other voltages for industry.

Real transformers

Real transformers are not 100 % efficient. Energy is lost by:

• Eddy currents in the iron core (reduced by laminating the core)
• Resistance heating in the copper windings

Exam tips

• Always write out V_p/V_s = n_p/n_s before substituting numbers.
• "Step-up" = secondary voltage higher = more secondary turns.
• P_loss = I²R — doubling the transmission voltage reduces current by half and losses by 75 %.