A three$-$winding transformer with N$1=10,$N$2=5$ and N$3=5$ turns uses a magnetic core withAm$=0\mathrm{.}639$ cm$2,$lm$=3\mathrm{.}12$ cm and r$=$mo$=5000.$ A square$-$wave voltage of $30$V amplitudealternating between $30$V and $+30$V and frequency of $100$kHz$,$ is applied to winding $1.$ Ignorethe leaking inductances and assume the flux waveform to be symmetric with the same positiveand negative peak amplitudes.

a$)$Calculate and draw the waveforms of magnetizing current, induced voltage in windings$2$ and $3$ synchronized to applied voltage waveform.

b$)$Calculate the self$-$inductance of each winding.

c$)$Calculate the peak flux density