Transformer Power Equation

Power into and out of a transformer

A transformer transfers electrical power between two circuits. The alternating potential difference applied across the primary coil provides the input. The secondary coil supplies the output circuit.

Electrical power is calculated using

$P=VI$

where $P$ is power in watts (W), $V$ is potential difference in volts (V), and $I$ is current in amperes (A). Therefore, the transformer's input power is $V_pI_p$, while its output power is .

The 100% efficiency assumption

An ideal transformer is 100% efficient. This means that none of the input power is dissipated to the surroundings, so the output power equals the input power:

$P_\text{input}=P_\text{output}$

Substituting $P=VI$ for each coil gives the transformer power equation:

$V_pI_p=V_sI_s$

Here, the subscript $p$ means primary and the subscript $s$ means secondary. The equation follows from conservation of energy: an ideal transformer can change potential difference and current, but it cannot create extra power.

How potential difference and current are linked

Because the two products must be equal, increasing the potential difference results in a corresponding decrease in current. For an ideal step-up transformer, $V_s>V_p$, so $I_s<I_p$. For an ideal step-down transformer, , so .

This comparison assumes that power is being transferred under the 100% efficiency condition. It does not mean that potential difference and current are always numerically equal or that they change by the same number of units.

Using the equation

First identify whether each value belongs to the primary or secondary coil. Then rearrange the equation for the required quantity. For example:

$I_p=\frac{V_sI_s}{V_p}$

A 100% efficient transformer that changes a primary potential difference of $230\ \text{V}$ to a secondary potential difference of $12\ \text{V}$ and supplies a secondary current of $2.5\ \text{A}$ has

$I_p=\frac{12\times2.5}{230}=0.13\ \text{A}$

The secondary power is $12\times2.5=30\ \text{W}$. Under the ideal assumption, the primary power is also $30\ \text{W}$, which provides a useful check on the answer.

Real transformers are not perfectly efficient because some energy is dissipated, so their output power is slightly less than their input power. The equality $V_pI_p=V_sI_s$ applies here because the specification explicitly assumes 100% efficiency.

Ideal-transformer equation

For a 100% efficient transformer:

$P_\text{input}=P_\text{output}$

Since $P=VI$: