Example 1
An ideal transformer has Np=200 and Ns=1000 with Vp=24.0V rms. Find Vs.
Vs= Vp NpNs=24.0×2001000=120V rms.
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Year 12 · SACE Stage 2
Transformers and power transmission
Use turn ratios and power balances to calculate voltage, current and line losses.
Method and worked examples
An alternating primary current produces changing magnetic flux in a transformer core. Flux linking the secondary coil induces its voltage. In an ideal transformer, VpVs=Ns/Np and input power equals output power: VpIp = VsIs. A step-up transformer raises voltage while lowering current for the same power; a step-down device does the reverse. Use consistent rms values for sinusoidal AC.
Steady DC does not produce a continuing secondary voltage after switching transients because its flux is unchanging. Real transformers lose energy through winding resistance, eddy currents, hysteresis and imperfect flux linkage. For transmitted power P, current is I=VP and cable heating is I2R. Raising transmission voltage therefore reduces current and resistive losses at the same delivered-power approximation, while insulation and infrastructure requirements still remain.
Example 1
Example 2
It supplies 240W at 120V. Find secondary and ideal primary currents.
Is=VsP=2.00A. Ip=VpP=10.0A. Higher secondary voltage corresponds to lower secondary current.
Watch out: In the ideal model, power is conserved, so increasing voltage lowers current proportionally.