In an ideal step-up transformer supplying a load, the secondary voltage is higher and the secondary current is lower than the primary current. Find the voltage ratio from the turns ratio, then use equality of input and output power to find the current.
The 2027 SEC G3 Physics K323 syllabus includes the ideal transformer equations and the advantages of transmitting electricity at high voltage. The examples below keep the turns and current relationships separate.
- Label the input coil primary and the output coil secondary.
- Use turns to find the voltage ratio.
- Use equal input and output power for the ideal model.
- Check that the current changes in the opposite direction to voltage.
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Use each relationship for its own job
A transformer uses an alternating current in its primary coil to produce a changing magnetic field. The changing field links to the secondary coil and induces an alternating voltage.
For an ideal transformer, Vₚ/Vₛ = Nₚ/Nₛ. Here V is voltage and N is the number of turns. The coil with more turns has the higher voltage.
For the ideal exam model, VₚIₚ = VₛIₛ. The voltage multiplied by the current gives the same power on both sides in the worked example.
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Worked example | Step 12 V up to 48 V
An ideal transformer has 150 primary turns and 600 secondary turns. Its primary voltage is 12 V a.c. and its primary current is 2.0 A when supplying a resistive load.
| Quantity | Primary | Secondary |
|---|---|---|
| Turns | 150 | 600 |
| Voltage | 12 V | 48 V |
| Current | 2.0 A | 0.50 A |
| Power | 24 W | 24 W |
The secondary has four times as many turns, so its voltage is 4 × 12 = 48 V. The input power is 12 × 2.0 = 24 W. Divide 24 W by 48 V to obtain a secondary current of 0.50 A.
Multiplying current by four as well would give 48 × 8 = 384 W at the output. The equal-power check catches the error.
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Apply the relationship to transmission
For a fixed transmitted power in a simple exam model, increasing the voltage reduces the current in the cables. The heating loss in a cable is I²R, where R is the cable resistance.
If the current falls to one quarter while the cable resistance stays the same, the heating loss falls to one sixteenth. This is why voltage matters even if the power to be delivered stays the same.
Try the reverse situation. If an ideal transformer steps 48 V down to 12 V while supplying 24 W to a load, the output current is 2.0 A. It is greater than the 0.50 A input current.
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Frequently asked questions
Does a transformer produce extra energy when it increases voltage?
The ideal model transfers the same power to the output. A real transformer also has losses.
Can I find the actual current from the turns alone?
The turns set the voltage ratio. You also need information such as one current, the power or the load to determine a current value.
What if there is a steady d.c. input?
A steady input does not maintain a changing magnetic field, so it cannot sustain a secondary voltage in the simple transformer model.
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