What is the transformation ratio of a transformer and how does it relate voltage, current and turns?

In one line

The transformation ratio \( K = N_2/N_1 = E_2/E_1 = I_1/I_2 \) tells how the transformer changes voltage and current: voltage scales with turns and current scales inversely.

Explained simply

Think of gears on a bicycle: a big gear turning a small gear gives more speed but less force. A transformer trades voltage for current the same way. Step the voltage up and the current goes down, because power in roughly equals power out.

Technically, the same flux links both windings, so the EMF per turn is the same in both. Hence \( E_1/N_1 = E_2/N_2 \). For an ideal transformer, input VA = output VA, so \( V_1I_1 = V_2I_2 \).

How it works

1. From the EMF equation, \( E_1 = 4.44fN_1\phi_m \) and \( E_2 = 4.44fN_2\phi_m \).
2. Dividing: \( E_2/E_1 = N_2/N_1 = K \).
3. For an ideal transformer, \( V_1 \approx E_1 \), \( V_2 \approx E_2 \) and \( V_1I_1 = V_2I_2 \), so \( I_1/I_2 = K \).
4. If \( K > 1 \): step-up (higher voltage, lower current). If \( K < 1 \): step-down. If \( K = 1 \): isolation transformer (1:1).
5. Some textbooks define \( K = N_1/N_2 \) instead. Always state your definition.

Key formula

\( K = \dfrac{N_2}{N_1} = \dfrac{E_2}{E_1} \approx \dfrac{V_2}{V_1} = \dfrac{I_1}{I_2} \)

\( N_1, N_2 \) = turns, \( E_1, E_2 \) = induced EMFs (V), \( V_1, V_2 \) = terminal voltages (V), \( I_1, I_2 \) = currents (A); \( K \) has no unit.

Quick example

A welding transformer steps 230 V down to a low voltage so that it can supply a very large current at the electrode. A power-station step-up transformer raises the generator voltage to transmission levels (for example 220 kV or 400 kV) so the line current, and hence \( I^2R \) loss, is much smaller.

Common mistakes

• Writing that current scales in the same ratio as voltage; it scales inversely.
• Thinking a step-up transformer gives more power; it gives more voltage but less current, and slightly less power due to losses.
• Mixing \( K = N_2/N_1 \) and \( K = N_1/N_2 \) within one answer.

How MU asks it

MU states numericals are not expected in this module, so questions are theory. Typical: "Define transformation ratio and state the relation between voltage, current and turns" (3–5 marks), often within the working-principle question. For full marks, define \( K \), derive \( E_2/E_1 = N_2/N_1 \) from the EMF equation, show \( I_1/I_2 = K \) from equal VA, and explain step-up/step-down.