(a) Figure P15:37 shows a three-winding transformer that can be treated as ideal.

Perfect coupling between all windings implies that \(v_{2}(t)=\frac{N_{2}}{N_{1}} v_{1}(t)\) and \(v_{3}(t)=\frac{N_{3}}{N_{1}} v_{1}(t)\).

Show that zero power loss means that \(N_{1} i_{1}(t)+N_{2} i_{2}(t\) ) \(+N_{3} i_{3}(t)=0\).
(b) Prove the result by simulating it using Multisim. Let \(N\) \({ }_{1}=1, N_{2}=2\), and \(N_{3}=3\). Put a \(1-\mathrm{k} \Omega\) resistor as a load on each output and feed the input \(i_{1}(t)\) with a 1000-Hz 1-A source.

Transcribed Image Text:

i(1) V(1) Nig ee IDEAL N2 N3 i(1) iz(t) V2(1) V3(t)