The Memory Trick
💡 V₁/V₂ = N₁/N₂
A transformer changes AC voltage using electromagnetic induction: a changing current in the primary coil creates a changing magnetic field, which induces a voltage in the secondary coil. The voltage ratio between primary and secondary exactly matches the ratio of the number of turns in each coil: V₁/V₂ = N₁/N₂. A transformer only works on AC — a steady DC current produces no changing flux, and therefore induces nothing.
Why It Works
Because an ideal transformer conserves power (P = V₁I₁ = V₂I₂), stepping voltage UP necessarily steps current DOWN by the same factor, and vice versa — you can't get more power out than you put in, so any gain in voltage always comes at the cost of a matching loss in current.
Step by Step
Working With Transformers
1
Step-up vs step-down
A step-up transformer has more secondary turns than primary turns (N₂ > N₁), producing higher output voltage. A step-down transformer has fewer secondary turns (N₂ < N₁), producing lower output voltage.
A transformer with twice as many secondary turns as primary turns doubles the voltage — but halves the current, keeping power conserved.
2
Power transmission relies on this tradeoff
Electricity is transmitted over long distances at very high voltage and correspondingly low current, specifically because resistive power loss in transmission lines (P = I²R) depends on the SQUARE of current — minimizing current minimizes losses far more effectively than minimizing voltage would.
Step-up transformers boost voltage to hundreds of thousands of volts for long-distance transmission, then step-down transformers reduce it back to safe, usable levels before reaching homes.
3
Why transformers can't work on DC
A transformer relies entirely on a CHANGING magnetic flux (from AC's constantly oscillating current) to induce voltage in the secondary coil — a steady DC current produces a constant, unchanging flux, inducing absolutely nothing.
This is a major historical reason AC won out over DC for large-scale power distribution — AC's compatibility with transformers made efficient long-distance transmission possible in a way DC of that era couldn't match.
🏥 Worked Example
A step-down transformer has 1000 turns on the primary and 100 turns on the secondary. If the primary voltage is 2400 V and primary current is 5 A, find the secondary voltage and current (assume an ideal transformer).
1
Find secondary voltage using the turns ratio: V₂ = V₁ × (N₂/N₁) = 2400 × (100/1000) = 240 V.
2
Find secondary current using power conservation: V₁I₁ = V₂I₂, so I₂ = V₁I₁/V₂ = (2400 × 5)/240.
3
Solve: I₂ = 12,000/240 = 50 A — notice current went UP by the same factor (10×) that voltage went DOWN, exactly preserving total power (both sides equal 12,000 W).
📌 Exam Application
Exams test correctly applying V₁/V₂ = N₁/N₂ alongside power conservation (V₁I₁ = V₂I₂) to solve for any unknown voltage, current, or turns value, and explaining why transformers require AC specifically.
⚠️ Most Common Transformers Mistakes
The most common trap is forgetting that current changes in the OPPOSITE direction from voltage in an ideal transformer — a step-up transformer that increases voltage necessarily decreases current by the same factor, since power must stay conserved.
✓ Quick Self-Test
1) Write the transformer turns-ratio formula relating voltage and number of turns. V₁/V₂ = N₁/N₂. 2) What distinguishes a step-up transformer from a step-down transformer? A step-up transformer has more secondary turns than primary (increasing voltage); a step-down transformer has fewer secondary turns (decreasing voltage). 3) Write the power conservation equation for an ideal transformer. P = V₁I₁ = V₂I₂. 4) Why does power transmission use very high voltage and low current over long distances? Because resistive power loss (P=I²R) depends on the square of current, so minimizing current (even at the cost of high voltage) dramatically reduces transmission losses. 5) Why can't a transformer work on steady DC current? A transformer requires a CHANGING magnetic flux to induce voltage; steady DC produces a constant flux, inducing nothing.