Electrical machines: transformers
Check a transformer with its turns ratio
Calculate secondary voltage, load current and reflected resistance, then use power balance to catch an inverted ratio.
What you’ll learn
- Use turns ratio for voltage and the inverse ratio for current.
- Check a loaded transformer with power balance and reflected resistance.
Before you start: Know Ohm’s law and power in a resistor. All voltages and currents below are RMS values for an ideal AC transformer.
In this guide 6 sections
1. Write down the model and the load
An ideal transformer has 600 turns on its primary winding and 120 turns on its secondary. The primary is supplied with 240 V RMS AC. A 12 Ω resistor is connected across the secondary. Find both currents and check the power balance.
“Ideal” means that we neglect winding resistance, core losses, leakage flux and magnetizing current. The load is purely resistive, so its power factor is 1. These assumptions are part of the problem, not properties we can assume for every real transformer.
Use subscripts p and s consistently. Before inserting numbers, write the voltage ratio in the same order as the turns ratio: Vs/Vp = Ns/Np. A quick prediction helps: fewer secondary turns should produce a lower secondary voltage.
2. Calculate the secondary voltage
Vs = 240 × (120 / 600) = 48 V RMS.
The ratio is 0.2, so this is a step-down transformer in the stated direction of operation. If you obtained 1200 V, you inverted the turns ratio. That answer contradicts the prediction made before calculating.
The turns ratio sets the ideal secondary voltage for a given primary voltage. It does not by itself set the secondary current: the connected load determines how much current is drawn.
3. Let the load determine current, then check power
Ohm’s law gives Is = 48 / 12 = 4 A RMS. Because the load is resistive, output power is Pout = 48 × 4 = 192 W. The ideal transformer has no losses, so the input must also supply 192 W.
Ip = 192 / 240 = 0.8 A RMS.
Check the current ratio: Ip/Is = 0.8 / 4 = 0.2 = Ns/Np.
Voltage decreases by a factor of five while the secondary current is five times the primary current. The transformer does not create power: the two changes balance. Applying the voltage ratio directly to current in the same direction would incorrectly predict a low voltage and a low output current while losing most of the power from an ideal model.
4. Reflect the load to the primary
There is another way to check the primary current. The input sees a reflected resistance Rin = (Np/Ns)² Rload. For this example, Rin = 5² × 12 = 300 Ω. Dividing 240 V by 300 Ω again gives 0.8 A.
The square is easy to miss. One factor comes from the voltage ratio and the other from the inverse current ratio. Reflected resistance describes the relationship seen at the input; it is not a claim that the actual 12 Ω load has physically become a 300 Ω resistor.
| Quantity | Primary | Secondary |
|---|---|---|
| Turns | 600 | 120 |
| Voltage, RMS | 240 V | 48 V |
| Current, RMS | 0.8 A | 4 A |
| Real power | 192 W input | 192 W output |
Try two variations
A. Change only the load
Replace the 12 Ω load with 24 Ω. Keep the ideal transformer and 240 V RMS input unchanged. Find the secondary voltage, both currents and output power.
Show the working
The ideal secondary voltage remains 48 V. Secondary current becomes 48 / 24 = 2 A. Output power is 96 W, so primary current is 96 / 240 = 0.4 A. Reflected resistance doubles to 600 Ω. The load change affects current and power, not the ideal turns ratio.
B. Step the voltage up
A different ideal transformer has 200 primary turns and 1000 secondary turns. With 24 V RMS at its input, the secondary feeds a 240 Ω resistor. Find output voltage and primary current.
Show the working
Vs = 24 × (1000 / 200) = 120 V RMS. The load current is 120 / 240 = 0.5 A and output power is 60 W. Primary current is 60 / 24 = 2.5 A. Higher output voltage accompanies lower output current, with 60 W on both sides.
Separate the ideal calculation from real machines
A real transformer draws some no-load current, dissipates heat and has load-dependent voltage regulation. Its ratings limit voltage, frequency and current. The ideal equations alone do not establish whether a particular physical unit can safely supply the calculated load.
A transformer transfers electrical energy between windings through changing magnetic flux. A motor converts electrical input into mechanical output; a generator converts mechanical input into electrical output. Turns-ratio calculations are a starting topic in electrical machines, but they do not replace torque, speed or efficiency analysis for rotating machines.
Formula reference: OpenStax, University Physics Volume 2, section 15.6. The loaded example and practice variations on this page were prepared for Padhnus.