1
GATE EE 2009
+2
-0.6
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

A
$$400$$ $$V$$
B
$$240$$ $$V$$
C
$$320$$ $$V$$
D
$$160$$ $$V$$
2
GATE EE 2009
+2
-0.6
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

A
$${{400} \over \pi }V$$
B
$$800$$ $$V$$
C
$${{4000} \over \pi }V$$
D
$${{800} \over \pi }V$$
3
GATE EE 2009
+2
-0.6
$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$\$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) evaluates to
A
-8
B
4
C
8
D
$$0$$
4
GATE EE 2009
+1
-0.3
The trace and determinant of a $$2 \times 2$$ matrix are shown to be $$-2$$ and $$-35$$ respectively. Its eigen values are
A
$$-30, -5$$
B
$$-37,-1$$
C
$$-7,5$$
D
$$17.5, -2$$
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