The circuit diagram shows a two-winding, lossless transformer with no leakage flux, excited from a current source, $$i(t)$$, whose waveform is also shown. The transformer has a magnetizing inductance of $$400/\pi \,\,mH.$$

If the waveform of $$i\left( t \right) = 10\sin \left( {100\pi t} \right)A,$$ the peak voltage across $$A$$ and $$B$$ with $$S$$ closed is

The circuit diagram shows a two-winding, lossless transformer with no leakage flux, excited from a current source, $$i(t)$$, whose waveform is also shown. The transformer has a magnetizing inductance of $$400/\pi \,\,mH.$$

The peak voltage across $$A$$ and $$B$$, with $$S$$ open is

$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) evaluates to

The trace and determinant of a $$2 \times 2$$ matrix are shown to be $$-2$$ and $$-35$$ respectively. Its eigen values are