Single-Phase Transformers: Necessity

Single-Phase Transformers: Necessity

1. What a Transformer Is

Transformer = static AC device (no moving parts) that transfers electrical energy between circuits at different voltage/current levels via mutual induction (changing flux), operating on AC only (DC gives no $dφ/dt$).

Single-phase transformer has two windings: primary (input) and secondary (output) on common laminated iron core, with turns ratio

(ideal).

2. Why It Is Necessary (exam list — 5 reasons)

Necessity	Explanation
1. Voltage transformation for transmission	Step-up at generating station (e.g., 11 kV → 220 kV) reduces $I$ for same $P$ ($P=VI$), so $I²R$ loss and voltage drop drastically reduce; step-down at distribution to 230V for consumer safety
2. Isolation	Galvanic isolation between primary and secondary (no conductor) ⇒ safety and noise/blocking DC
3. Impedance matching	Reflects load impedance as

⇒ match source to load for maximum power transfer (audio, RF) |
| 4. Measurement | Instrument transformers: Current transformer (CT) steps down high $I$ to 5A for meter, Potential transformer (PT) steps down high $V$ to 110V for metering/protection safely |
| 5. Power system flexibility | Allows multiple voltage levels in same grid (generation, transmission, distribution, utilisation) via tap changers |

Without transformer, AC transmission would be as inefficient as DC at low voltage (historical War of Currents, Westinghouse/Tesla AC won due to transformer).

3. Worked Illustration

Generation 11kV → step-up to 220kV for 100km line: current reduces 20× ⇒ loss reduces 400× (I²R) ⇒ same copper can carry 20× power.

Need to match 8Ω speaker to amplifier output impedance 1000Ω: use transformer turns ratio √(1000/8)=11.2 ⇒ N1:N2≈11:1 ⇒ amplifier sees 8·(11)²≈1000Ω.

4. Exam Points

• Define transformer as static mutual induction device (AC only) — 3-5 marks, very frequent.
• List 4–5 necessities (voltage transformation for transmission, isolation, impedance matching, measurement) — 5-7 marks, very frequent (the most common necessity question).
• Show $V_1/V_2=N_1/N_2$ — 3 marks, frequent.
• Explain why step-up reduces $I²R$ loss — 5 marks, frequent.