Transformer — working principle and calculate turns ratio for step-up/down

Question

Explain the working principle of a transformer. A transformer has 500 turns in the primary coil and 5000 turns in the secondary. If the primary voltage is 220 V, find the secondary voltage. Is this a step-up or step-down transformer?

(NCERT Class 12, Chapter 7)

Solution — Step by Step

A transformer works on the principle of mutual induction. When alternating current flows through the primary coil, it creates a changing magnetic flux in the soft iron core. This changing flux links with the secondary coil and induces an EMF in it (Faraday’s law).

Key requirement: the input must be AC — a transformer does not work with DC because DC produces constant flux (no change = no induction).

For an ideal transformer (no energy losses):

\frac{V_s}{V_p} = \frac{N_s}{N_p}

where $V_s$ , $V_p$ are secondary and primary voltages, and $N_s$ , $N_p$ are the number of turns.

Given: $N_p = 500$ , $N_s = 5000$ , $V_p = 220$ V.

V_s = V_p \times \frac{N_s}{N_p} = 220 \times \frac{5000}{500} = 220 \times 10 = \mathbf{2200 \text{ V}}

Since $V_s > V_p$ (and $N_s > N_p$ ), this is a step-up transformer.

For an ideal transformer, power is conserved: $V_p I_p = V_s I_s$ .

If primary current is, say, 10 A, then secondary current:

I_s = \frac{V_p I_p}{V_s} = \frac{220 \times 10}{2200} = 1 \text{ A}

Voltage goes up, current goes down — energy is conserved.

Why This Works

The transformer transfers energy from one circuit to another through the shared magnetic flux in the iron core. The turns ratio determines how the voltage is scaled. More turns in the secondary means each turn “picks up” a share of the flux change, and the EMFs add up.

Real transformers have losses — eddy currents in the core, resistive heating in coils (copper loss), and magnetic hysteresis. Efficiency of good power transformers is typically 90-99%.

Alternative Method — Identifying Step-up vs Step-down Quickly

Just compare $N_s$ and $N_p$ :

$N_s > N_p$ → Step-up (voltage increases, current decreases)
$N_s < N_p$ → Step-down (voltage decreases, current increases)

For NEET, remember the power relation: $V_p I_p = V_s I_s$ . This means a step-up transformer increases voltage but decreases current by the same factor. Examiners often ask: “Does a step-up transformer violate energy conservation?” The answer is no — what you gain in voltage, you lose in current.

Common Mistake

A frequent board exam error: students say a transformer works with DC. It does NOT. DC produces constant flux, so $d\Phi/dt = 0$ , and no EMF is induced in the secondary. If you connect DC to a transformer primary, you only get a brief pulse of EMF when the circuit is switched on or off — not a sustained output.

Question

Solution — Step by Step

Why This Works

Alternative Method — Identifying Step-up vs Step-down Quickly

Common Mistake

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