Ideal TransformerJEE Main

Concept

A transformer uses mutual induction between two coils on a shared iron core to change an AC voltage. The voltage ratio equals the turns ratio; an ideal transformer conserves power, so stepping voltage up steps current down by the same factor.

Key formula

Derivation

The same changing flux links every turn, so each coil's EMF is proportional to its turns: $V_s/V_p = N_s/N_p$.

With no losses, input power equals output power ($V_pI_p = V_sI_s$), which forces the current ratio to be the inverse of the turns ratio. More turns ⇒ higher voltage but lower current.

Scenarios to explore

• Ideal Transformer — Turns ratio steps voltage up or down.

Real-world applications

• Power transmission (step-up to reduce $I^2R$ losses).
• Phone and laptop chargers (step-down).
• Impedance matching in audio circuits.

JEE exam tips

• Step-up for voltage means step-down for current (power constant).
• Real transformers lose energy to eddy currents, hysteresis and copper resistance.
• Transmission at high voltage minimises $I^2R$ heating in the wires.

Common mistakes

• Inverting the turns ratio for voltage.
• Thinking a transformer works on DC (it needs changing flux).
• Assuming it can create power — it only converts it.

Exam traps to avoid

• Transformers only work with alternating current.
• Efficiency is high but never 100% in practice.