Transformers | Physics

📖 In-Depth Theory

How Transformers Work

A TRANSFORMER changes the voltage of an alternating current supply.

CONSTRUCTION:

Two coils of wire wound onto an IRON CORE:

PRIMARY COIL: connected to the input AC supply (Vₚ).

SECONDARY COIL: provides the output voltage (Vₛ).

SOFT IRON CORE: channels magnetic flux between the coils efficiently.

OPERATION (mutual induction):

1. AC in primary coil → ALTERNATING MAGNETIC FIELD in the iron core.

2. Alternating magnetic flux threads through the secondary coil.

3. Changing flux induces an EMF in the secondary coil (Faraday's Law).

4. Output voltage depends on the ratio of turns.

CRITICAL: Transformers only work with AC — DC produces a CONSTANT magnetic flux, which does not change and therefore induces no emf.

Transformer Equations

TURNS RATIO EQUATION:

Vₛ/Vₚ = Nₛ/Nₚ

Where:

Vₛ = secondary (output) voltage (V)

Vₚ = primary (input) voltage (V)

Nₛ = number of turns on secondary coil

Nₚ = number of turns on primary coil

STEP-UP TRANSFORMER: Nₛ > Nₚ → Vₛ > Vₚ (increases voltage).

STEP-DOWN TRANSFORMER: Nₛ < Nₚ → Vₛ < Vₚ (decreases voltage).

POWER CONSERVATION (for ideal transformer):

Power in = Power out

Vₚ × Iₚ = Vₛ × Iₛ

Therefore: Vₚ/Vₛ = Iₛ/Iₚ

Step-up voltage → step-down current (and vice versa).

EXAMPLE:

Primary: 230 V, 100 turns. Secondary: what voltage if 500 turns?

Vₛ = Vₚ × (Nₛ/Nₚ) = 230 × (500/100) = 1150 V.

Transformers in the National Grid

NATIONAL GRID uses transformers to transmit electricity efficiently.

POWER STATION → STEP-UP TRANSFORMER → HIGH VOLTAGE TRANSMISSION → STEP-DOWN TRANSFORMER → CONSUMERS

Typically: 25 kV (power station) → 400 kV (transmission) → 33 kV (industrial) → 11 kV → 230 V (homes).

WHY HIGH VOLTAGE FOR TRANSMISSION:

P = V × I. To transmit a given power P at high voltage → LOW current needed.

P_lost = I² × R (power lost in cable resistance).

Low current → much less power wasted in transmission cables.

EXAMPLE:

Transmit 100 MW at 1000 V vs 1,000,000 V:

At 1000 V: I = 100,000 A → P_loss = 100,000² × R (enormous).

At 1,000,000 V: I = 100 A → P_loss = 100² × R (10,000 times less).

ENERGY LOSSES IN REAL TRANSFORMERS:

Eddy currents in the iron core — reduced by using laminated core.

Resistance heating in coil wires — use thick copper wire.

Magnetic flux leakage — tight winding, soft iron core.

Real transformers: ~95–99% efficient.

⚠️ Common Mistake

Transformers only work with AC — not DC. DC produces constant flux → no change → no induced emf. Step-up transformer increases VOLTAGE but DECREASES current (power is conserved). National Grid uses high voltage to REDUCE current → reduces I²R power losses in transmission cables.

📐 Variables

VₚPrimary voltage (Vₚ) is measured in volts (V)

VₛSecondary voltage (Vₛ) is measured in volts (V)

NₚNumber of primary turns (Nₚ) is measured in ()

NₛNumber of secondary turns (Nₛ) is measured in ()

📐 Key Equations

Vₛ/Vₚ = Nₛ/Nₚ (turns ratio equation)

Vₚ × Iₚ = Vₛ × Iₛ (power conservation in ideal transformer)

📌 Key Note

Transformer: AC in primary → alternating flux in iron core → emf induced in secondary. Turns ratio: Vs/Vp = Ns/Np. Step-up: Ns > Np. Power conservation: Vp×Ip = Vs×Is. National Grid: step-up to ~400 kV for transmission (low current → less I²R loss), step-down for consumers. AC only — DC gives constant flux, no induction.

🎯 Matching Activity — Transformer Equations

Match each transformer scenario to the correct calculation. — drag the symbols on the right to match the component names on the left.

Step-up transformer

Drop here

Step-down transformer

Drop here

National Grid transmission

Drop here

Power conservation

Drop here

Step-up to ~400 kV → low current → low I²R losses in cables

Ns < Np → output voltage less than input voltage

Vp × Ip = Vs × Is — higher voltage means lower current

Ns > Np → output voltage greater than input voltage

⚽ FIFA Worked Examples

Transformer Voltage

A transformer has 200 primary turns and 800 secondary turns. Input voltage = 230 V. Find the output voltage.

F

Vs/Vp = Ns/Np

I

Vp = 230 V, Np = 200, Ns = 800

F

Vs = Vp × (Ns/Np) = 230 × (800/200) = 230 × 4

A

Vs = 920 V (step-up transformer)

⭐ Higher Tier Only

HT only — use the turns ratio equation to calculate transformer voltages and turns. Apply power conservation to find current in transformer circuits. Explain why the National Grid uses high voltage transmission and calculate power losses at different voltages.

🔬 Triple Science Only

Transformers (HT only, physics only) — not in Combined Science.

🎯 Test Yourself

Question 1 of 2

1. Why can't transformers work with direct current (DC)?

2. Why does the National Grid transmit electricity at very high voltages?

⭐ How Well Do You Understand This Topic?

Be honest with yourself — this helps you know what to revise!

Don't get it Getting there Nailed it!

🤖 Ask MrBadmus

Stuck? Just ask! 💬

I'll use CFIFA for calculations and flag Higher/Triple content clearly.