Transformer Equations
2 guided lessons · 18 checks · 6. Magnetism and Electromagnetism → Electromagnetic Induction
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Lesson 1 of 2
The turns-ratio equation in use
One relationship runs every transformer calculation: primary voltage over secondary voltage equals primary turns over secondary turns. Read the turns, read the known voltage, and the unknown comes out — up for a step-up with more secondary turns, down for a step-down with fewer.
What you know already
Two equations run every transformer problem: the turns ratio links voltages to turns, and the ideal power balance VpIp = VsIs links voltage to current. This note drills both — step-up arithmetic with sanity checks, and the grid's trade of voltage for current.
Key points of understanding
- The relationship is: primary voltage / secondary voltage = primary turns / secondary turns.
- The input voltage is across the primary; the output is across the secondary.
- Rearranged, secondary voltage = primary voltage × secondary turns / primary turns.
- More secondary turns than primary means the voltage is stepped up.
- Substitute in the ratio form and keep units consistent — volts in, volts out.
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1.The turns-ratio equation in use
One relationship runs every transformer calculation: primary voltage over secondary voltage equals primary turns over secondary turns. Read the turns, read the known voltage, and the unknown comes out — up for a step-up with more secondary turns, down for a step-down with fewer.
Key points
- The relationship is: primary voltage / secondary voltage = primary turns / secondary turns.
- The input voltage is across the primary; the output is across the secondary.
- Rearranged, secondary voltage = primary voltage × secondary turns / primary turns.
- More secondary turns than primary means the voltage is stepped up.
- Substitute in the ratio form and keep units consistent — volts in, volts out.
First pass
Voltage follows turns: divide the primary voltage by the turn ratio and you have the secondary voltage. Double the secondary turns and the voltage doubles with them.
Analogy — The turns ratio is a recipe scale: 800 turns instead of 20 is forty times the recipe, so the output voltage is forty times the per-turn serving.
Exam pointer — Write the relationship FIRST in ratio form, then substitute — method marks live in the equation line, not the arithmetic.
Going deeper
The ratio form Vp/Vs = Np/Ns expresses the shared per-turn induced voltage: every turn sees the same changing flux, so voltages partition exactly as turns do. Solving for Vs gives Vp × Ns/Np, and the step-up/step-down classification follows from comparing Ns with Np before any arithmetic.
Analogy — The core field is one message read by every turn: how many readers you place on each side decides how the total voltage is shared out.
Exam pointer — Sanity-check the answer against the classification: a step-up result larger than the input for Ns > Np — a mismatch means the ratio was inverted.
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2.The ideal transformer equation and the grid's arithmetic
Assume a perfectly efficient transformer and power balances across it: input power equals output power, so Vp × Ip = Vs × Is. Step the voltage up and the current steps down by the same factor — the arithmetic that makes high-voltage transmission worthwhile.
Key points
- For 100% efficiency: input power = output power.
- In symbols: Vp × Ip = Vs × Is.
- Stepping the voltage up steps the current down by the same factor.
- Stepping the voltage down lets the secondary deliver a larger current.
- The relationship pairs with the turns ratio to solve full transformer problems.
First pass
Power in equals power out for an ideal transformer: raise the voltage and the current shrinks to pay for it; lower the voltage and the current grows.
Analogy — A seesaw in money terms: the transformer is a currency exchange between volts and amps at a fair rate — more of one means less of the other.
Exam pointer — Quote the power balance with symbols — VpIp = VsIs — and label which side is input; unlabelled equations score half.
Going deeper
The ideal equation is energy conservation per unit time: with no losses, the input power VpIp must equal the delivered power VsIs, so current and voltage transform inversely. Combined with the turns ratio, the pair determines all four quantities — which is how grid designers trade voltage against current to keep cable heating down.
Analogy — The transformer is a two-way tap: what it gives the output in voltage it takes back in current, and the power ledger always balances.
Exam pointer — The 100% efficiency assumption is stated in the specification — say 'assuming 100% efficiency' when deploying VpIp = VsIs.
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