Transformer
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Direct answer
Mains electricity reaches an Indian home at 220 V, yet a doorbell needs a few volts and a transmission line wants several lakh — the transformer performs both conversions with no moving parts. An alternating current in the primary sets up changing flux in a laminated soft-iron core, inducing an emf in the secondary by mutual induction: E_s/E_p = N_s/N_p, with an ideal machine conserving power so I_s/I_p = N_p/N_s. Step-up raises voltage and lowers current; step-down does the reverse; and DC gives a steady flux and no emf — the machines are AC-only, which is why long-distance transmission steps the voltage up: halving the current quarters the line's I^2R loss.
What you must remember
- Turns ratio: E_s/E_p = N_s/N_p; the voltage ratio equals the turns ratio, and for an ideal transformer I_p V_p = I_s V_s so currents go the opposite way.
- Step-up versus step-down: N_s > N_p raises voltage and lowers current; N_s < N_p does the reverse — a transformer changes voltage and current, never frequency and never DC power.
- Why AC only: a steady DC flux does not change, so dΦ/dt = 0 and no emf appears in the secondary; feeding DC can also burn the primary, whose opposition to current is then only its small resistance.
- Four losses: copper loss I^2R in the windings (reduced by thick conductors), eddy-current heating (reduced by laminations), hysteresis loss per cycle (reduced by soft silicon steel with a narrow loop), and flux leakage (reduced by a closed core winding both coils on a common limb).
- Efficiency: real power transformers commonly run above 95 per cent, large units near 99.
- Transmission logic: line loss = I^2R_line; stepping voltage up by a factor of n cuts current n-fold and loss n^2-fold — the entire case for high-voltage transmission.
A doorbell transformer, accounted to the last decimal
A doorbell transformer has N_p = 2200 turns on the primary connected to the 220 V mains, and N_s = 100 turns on the secondary. The secondary voltage follows the ratio: E_s = 220 × (100/2200) = 10 V. The bell draws 2 A at 10 V — 20 W — and an ideal transformer would draw exactly 20 W from the mains, I_p = 20/220 ≈ 0.09 A. Now run the machine backwards: connect 10 V AC to the 100-turn side and the 2200-turn side delivers 220 V — the same device is a step-up transformer now, because "primary" only names the coil you feed. And run the loss bookkeeping: if this real unit is 90 per cent efficient, the primary draws 22.2 W, the extra 2.2 W shared among copper heating, eddies in the laminations and hysteresis in the iron every cycle. Each loss has a named cure, and matching loss to cure is half the marks in this chapter.
Frequently asked questions
On what principle does a transformer work?
Mutual induction: an alternating primary current produces a changing core flux that links the secondary and induces an emf proportional to its number of turns.
Why cannot a transformer work on direct current?
A steady DC produces a constant flux and no induced emf; worse, the primary may overheat for lack of inductive opposition.
How does stepping up voltage reduce transmission losses?
Power at higher voltage needs lower current, and the line's heat loss I^2R falls as the square of that current reduction — the reason grids run at very high voltages.
Which losses occur in a real transformer?
Copper (I^2R) losses in the windings, eddy-current heating in the core, hysteresis loss in the iron each cycle, and flux leakage that fails to link both coils.
Can the same transformer be used as step-up and step-down?
Yes — the coil you feed is the primary; reversing the roles inverts the turns ratio, so a 220 V-to-10 V unit used backwards steps 10 V up to 220 V.