1
GATE ECE 1997
Subjective
+5
-0
GATE ECE 1997 Network Theory - State Equations For Networks Question 2 English 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

2
GATE ECE 1997
MCQ (Single Correct Answer)
+3
-0.9
In the circuit of Fig., the current iD through the ideal diode (zero cut in voltage and zero forward resistance) equals GATE ECE 1997 Network Theory - Miscellaneous Question 2 English
A
0 A
B
4 A
C
1 A
D
None of the above
3
GATE ECE 1997
MCQ (Single Correct Answer)
+2
-0.6
In the circuit of Fig., energy absorbed by the 4 Ω registor in the time interval (0,$$\infty$$) is GATE ECE 1997 Network Theory - Miscellaneous Question 3 English
A
36 Joules
B
16 Joules
C
256 Joules
D
None of the above
4
GATE ECE 1997
Subjective
+5
-0
In the circuit of Fig., all currents and voltage are sinusoids of frequency $$\omega $$ rad/sec. GATE ECE 1997 Network Theory - Sinusoidal Steady State Response Question 14 English

(a) Find the impedance to the right of $$\left( {A,\,\,\,\,\,\,B} \right)$$ at $$\omega \,\,\, = \,\,\,\,0$$ rad/sec and $$\omega \,\,\, = \,\,\,\,\infty $$ rad/sec.

(b) If $$\omega \,\,\, = \,\,\,\,{\omega _0}$$ rad/sec and $${i_1}\left( t \right) = \,\,{\rm I}\,\,\,\sin \,\left( {{\omega _0}t} \right)\,{\rm A},$$ where $${\rm I}$$ is positive, $${{\omega _0}\,\, \ne \,\,0}$$, $${{\omega _0}\,\, \ne \,\,\infty }$$, then find $${\rm I}$$, $${{\omega _0}}$$ and $${i_2}\left( t \right)$$

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