1
GATE ECE 2009
+1
-0.3
If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}} \,\,dz$$ is given
A
$$2\,\pi \,{C_1}$$
B
$$2\,\pi \,(1 + {C_0})$$
C
$$2\,\pi \,j\,{C_1}$$
D
$$2\,\pi \,j\,(1 + {C_0})$$
2
GATE ECE 2009
+1
-0.3

In the interconnection of ideal sources shown in the figure, it is known that the 60V source is absorbing power.

Which of the following can be the value of the current source I?

A
10 A
B
13 A
C
15 A
D
18 A
3
GATE ECE 2009
+2
-0.6
In the circuit shown, what value of RL maximizes the power delivered to RL?
A
$$2.4\Omega$$
B
$$\frac8{3}\Omega$$
C
$$4\Omega$$
D
$$6\Omega$$
4
GATE ECE 2009
+2
-0.6
The time domain behavior of an RL circuit is represented by $$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm{dt}}+\mathrm{Ri}\;=\;{\mathrm V}_0\left(1\;+\;\mathrm{Be}^{-\mathrm{Rt}/\mathrm L}\;\sin\;\mathrm t\right)\mathrm u\left(\mathrm t\right)$$\$ For an initial current of i(0) = $$\frac{{\mathrm V}_0}{\mathrm R}$$, the steady state value of the current is given by
A
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{{\mathrm V}_0}{\mathrm R}$$
B
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{2{\mathrm V}_0}{\mathrm R}$$
C
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{{\mathrm V}_0}{\mathrm R}\left(1+\mathrm B\right)$$
D
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{2{\mathrm V}_0}{\mathrm R}\left(1+\mathrm B\right)$$
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