Multiple choice

Assume that the switch S is in position 1 for a long time and thrown to position 2 at t = 0.

I1 (s) and I2 (s) are the Laplace transforms of i1 (t) and i2 (t) respectively. The equation for the loop current I1 (s) and I2 (s) for the circuit shown in figure Q.33-34, after the switch is brought from position 1 to position 2 at t = 0, are

  1. $\left[ \begin{array} \ R+Ls+\dfrac{1}{Cs} & -Ls \\\\ -Ls & R+Ls+\dfrac{1}{Cs} \end{array} \right] \left[ \begin{array} \ I_1 & (s) \\\\ I_2 & (s) \end{array} \right] = \left[ \begin{array} -\dfrac{V}{S} \\\\ 0 \end{array} \right] $
  2. $\left[ \begin{array} \ R+Ls+\dfrac{1}{Cs} & -Ls \\\\ -Ls & R+\dfrac{1}{Cs} \end{array} \right] \left[ \begin{array} \ I_1 & (s) \\\\ I_2 & (s) \end{array} \right] = \left[ \begin{array} \ -\dfrac{V}{S} \\\\ 0 \end{array} \right] $
  3. $\left[ \begin{array} \ R+Ls+\dfrac{1}{Cs} & -Ls \\\\ -Ls & R+Ls+\dfrac{1}{Cs} \end{array} \right] \left[ \begin{array} \ I_1 & (s) \\\\ I_2 & (s) \end{array} \right] = \left[ \begin{array} \ \dfrac{V}{S} \\\\ 0 \end{array} \right] $
  4. $\left[ \begin{array} \ R+Ls+\dfrac{1}{Cs} & -Ls \\\\ -Ls & R+Ls+\dfrac{1}{Cs} \end{array} \right] \left[ \begin{array} \ I_1 & (s) \\\\ I_2 & (s) \end{array} \right] = \left[ \begin{array} \ -\dfrac{V}{S} \\\\ 0 \end{array} \right] $
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