Electricity and magnetism

Transformers and generators

A generator converts mechanical to electrical energy by induction; a transformer changes AC voltage according to its turns ratio.

\frac{U_s}{U_p}=\frac{N_s}{N_p},\qquad U_pI_p\simeq U_sI_s

Definition: Ideal transformer

Two coils on a common core are linked by changing magnetic flux. For an ideal transformer, RMS voltage ratio equals turns ratio, $U_s/U_p=N_s/N_p$ , while power conservation gives $U_pI_p=U_sI_s$ . A transformer needs changing flux, usually supplied by AC. A generator induces emf as a rotating coil changes its flux; for $N$ turns of area $A$ rotating at angular speed $\omega$ in $B$ , $\mathcal E_0=NBA\omega$ .

Adjust the controls and drag the view to explore the topic’s quantitative field, orbit, or waveform.

Reading the model

Example: Worked example

An ideal transformer has $N_p=500$ , $N_s=1000$ , $U_p=12$ V, and a load current $I_s=0.30$ A. Find $U_s$ and $I_p$ .

Solution

The turns ratio gives $U_s=12(1000/500)=24$ V. Output power is $24(0.30)=7.2$ W, so $I_p=7.2/12=0.60$ A.

In a simple AC generator, flux through a rotating coil changes with time, so induced emf reverses periodically. Electrical energy does not appear spontaneously: an external drive supplies mechanical work, and the load receives energy through current. For an ideal transformer, power conservation gives $U_pI_p=U_sI_s$ ; stepping voltage up by the turns ratio reduces secondary current correspondingly. Real devices are less than 100% efficient because of winding resistance, eddy currents, and flux leakage.

Quick check

An ideal transformer has $N_s=2N_p$ . Then:

An ideal transformer has $N_s=3N_p$ . The secondary voltage is:

References

Young, Freedman (2019). University Physics