Transformer power equation: Vp Ip = Vs Is

Primary p.d. × primary current = secondary p.d. × secondary current. In symbols, V_p I_p = V_s I_s. V_p and V_s are in volts (V), and I_p and I_s are in amperes (A). AQA, Edexcel and OCR all print it on the GCSE exam sheet; only AQA marks it as Higher tier.

Equation

V_p I_p = V_s I_s

Symbol	Quantity	Unit
`V_p`	primary potential difference	V
`I_p`	primary current	A
`V_s`	secondary potential difference	V
`I_s`	secondary current	A

What each specification says

Exam board	Status	Equation
AQA Physics (8463)	Given on the sheet · Higher tier only	`V_p I_p = V_s I_s`
AQA Combined Science (8464)	Given on the sheet · Higher tier only	`V_p I_p = V_s I_s`
Edexcel Physics (1PH0)	Given on the sheet	`V_p I_p = V_s I_s`
Edexcel Combined Science (1SC0)	Given on the sheet	`V_p I_p = V_s I_s`
OCR Gateway Physics A (J249)	Given on the sheet	`V_p I_p = V_s I_s`
OCR Twenty First Century Physics B (J259)	Given on the sheet	`V_p I_p = V_s I_s`

Calculator: V_p I_p = V_s I_s

Power in equals power out

Each side of the equation is a power, because electrical power is potential difference times current. So the equation says the power going into the primary coil equals the power coming out of the secondary coil.

That is only true for a perfect transformer that wastes nothing. Edexcel's list says the equation applies to a transformer that is 100% efficient. Real transformers lose a little energy as heat, but good ones come close, so GCSE questions treat them as perfect.

The result is a trade. If a transformer raises the voltage 20 times, it cuts the current to one twentieth. It cannot raise both.

Tier and course, board by board

Every board prints the same form, V_p I_p = V_s I_s, and puts it on its given list. The tier differs.

AQA Physics (8463) and AQA Combined Science Trilogy (8464): Higher tier.
Edexcel Physics (1PH0) and Edexcel Combined Science (1SC0): both tiers.
OCR Gateway (J249) and OCR Twenty First Century (J259): both tiers.

So a Foundation student on Edexcel or OCR can meet it, while an AQA Foundation student will not. Every GCSE physics paper from 2025 onwards includes an equation sheet, and this one is on it. The AQA equation list and the OCR Gateway list show where it sits.

Why the grid uses high voltage

Cables have resistance, and a current heats them. The heating power grows with the square of the current, as P = I²R shows. Halve the current and the heat loss falls to a quarter.

A step-up transformer at the power station raises the voltage to many thousands of volts. By this equation, the current drops by the same factor, so far less energy is lost on the way. The turns ratio equation tells you how many turns of wire give that change.

Worked examples

I_s

I_s = V_p I_p ÷ V_s
I_s = 230 × 0.2 ÷ 11.5
I_s = 46 ÷ 11.5
I_s = 4 A

4 A

I_s

Change the primary current to amps: 400 mA = 0.4 A
I_s = V_p I_p ÷ V_s
I_s = 230 × 0.4 ÷ 4600
I_s = 92 ÷ 4600
I_s = 0.02 A

0.02 A

V_s

Change the primary voltage to volts: 11 kV = 11 000 V
V_s = V_p I_p ÷ I_s
V_s = 11 000 × 20 ÷ 800
V_s = 220 000 ÷ 800
V_s = 275 V

275 V

Common mistakes

Pairing the wrong values. V_p must multiply I_p, the current in the same coil, never the secondary current.
Thinking a higher output voltage means a higher output current too. In this equation, one goes up as the other goes down.
Forgetting to change kV into V. An 11 kV supply entered as 11 gives a secondary voltage 1000 times too small.
Using it without thought when a question says the transformer wastes energy. Then the output power is less than the input, and the two sides are no longer equal.

Practise solving for I_s or V_s in the Equation Rearranger.

Questions people ask

Does this equation work for direct current?

No. A transformer needs alternating current to make a changing magnetic field. With a steady current, the secondary coil gets no potential difference.

Which transformer equation should I use?

Use V_p I_p = V_s I_s when a question talks about currents or power. Use the turns ratio when it gives the number of turns on the coils.