1
GATE ECE 2020
MCQ (Single Correct Answer)
+2
-0.67

$$ \text { For the given circuit, which one of the following is the correct state equation? } $$

GATE ECE 2020 Network Theory - State Equations For Networks Question 1 English
A

$\frac{d}{d t}\left[\begin{array}{l}v \\ i\end{array}\right]=\left[\begin{array}{ll}-4 & -4 \\ -2 & -4\end{array}\right]\left[\begin{array}{l}v \\ i\end{array}\right]+\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]\left[\begin{array}{l}i_1 \\ i_2\end{array}\right]$

B

$\frac{d}{d t}\left[\begin{array}{c}v \\ i\end{array}\right]=\left[\begin{array}{cc}-4 & 4 \\ -2 & -4\end{array}\right]\left[\begin{array}{c}v \\ i\end{array}\right]+\left[\begin{array}{ll}0 & 4 \\ 4 & 0\end{array}\right]\left[\begin{array}{l}i_1 \\ i_2\end{array}\right]$

C

$\frac{d}{d t}\left[\begin{array}{l}v \\ i\end{array}\right]=\left[\begin{array}{cc}4 & -4 \\ -2 & -4\end{array}\right]\left[\begin{array}{l}v \\ i\end{array}\right]+\left[\begin{array}{ll}0 & 4 \\ 4 & 4\end{array}\right]\left[\begin{array}{l}i_1 \\ i_2\end{array}\right]$

D

$\frac{d}{d t}\left[\begin{array}{l}v \\ i\end{array}\right]=\left[\begin{array}{cc}-4 & -4 \\ -2 & 4\end{array}\right]\left[\begin{array}{l}v \\ i\end{array}\right]+\left[\begin{array}{ll}4 & 4 \\ 4 & 0\end{array}\right]\left[\begin{array}{l}i_1 \\ i_2\end{array}\right]$

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