Ideal transformer power

A transformer transfers electrical power from its primary side to its secondary side. An ideal transformer is 100% efficient: no power is lost, so the power supplied to the primary equals the power delivered by the secondary.

Electrical power is the product of voltage and current. For an ideal transformer:

Here, $$I_{\mathrm{p}}$$ and $$V_{\mathrm{p}}$$ are the primary current and voltage; $$I_{\mathrm{s}}$$ and $$V_{\mathrm{s}}$$ are the secondary current and voltage. Current is measured in amperes and voltage in volts, giving power in watts.

Calculating ideal transformer current

The power equation can be rearranged to find an unknown voltage or current. For example, dividing both sides by $$V_{\mathrm{s}}$$ gives the secondary current:

Suppose the primary voltage is $$120\ \mathrm{V}$$ and its current is $$2\ \mathrm{A}$$. The input power is $$240\ \mathrm{W}$$, so the secondary also delivers $$240\ \mathrm{W}$$. If the secondary voltage is $$240\ \mathrm{V}$$, its current is $$1\ \mathrm{A}$$.

For a given transferred power, stepping up the voltage reduces the current: in this example, doubling the voltage halves the current. Conversely, stepping down the voltage increases the current. The voltage and current change in opposite proportions so that their product remains the same.