1
GATE ECE 1997
Subjective
+5
-0

In the circuit of Fig. when R = 0 Ω, the current iR equals 10 A.

(a) Find the value of R for which it absorbs maximum power.

(b) Find the value of E.

(c) Find v2 when R = $$\infty$$ ( open circuit)

2
GATE ECE 1997
Subjective
+5
-0
For the circuit shown in Fig. choose state variables $$X_1,\;X_2,\;X_3$$ to be $$i_{L1}\left(t\right),\;v_{C2}\left(t\right),\;i_{L3}\left(t\right)$$

(a) Write the state equations

$$\begin{bmatrix}{\dot X}_1\\{\dot X}_2\\{\dot X}_3\end{bmatrix}\;=\;A\;\begin{bmatrix}X_1\\X_2\\X_3\end{bmatrix}\;+\;B\left[e\left(t\right)\right]$$\$

(b) If e(t) = 0, t $$\geq$$ 0, $$i_{L1}\left(0\right)\;=\;0,\;v_{C2}\left(0\right)\;=\;0,\;i_{L3}\left(0\right)\;=\;1A,$$ then what would the total energy dissipated in the registors in the interval $$\left(0,\infty\right)$$ be

3
GATE ECE 1997
+3
-0.9
In the circuit of Fig., the current iD through the ideal diode (zero cut in voltage and zero forward resistance) equals
A
0 A
B
4 A
C
1 A
D
None of the above
4
GATE ECE 1997
+2
-0.6
In the circuit of Fig., energy absorbed by the 4 Ω registor in the time interval (0,$$\infty$$) is
A
36 Joules
B
16 Joules
C
256 Joules
D
None of the above
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