The Problems (don't click until you are ready

• Problem 1. (50 pts)

  Find the current $i(t)$ through the $5\Omega$ resistor in the circuit shown in the figure below. Here the voltage source is $v_0(t)=10\sqrt{2}\cos 2t$ and the current source is $i_0(t)=2\sqrt{2}\cos(3t+45^\circ)$.

  

• Problem 2. (50 pts)

  In the circuit shown in the figure below, $R_1=R_2=15 k\Omega$, $R_3=30 k\Omega$, $C=50 \mu F$, and the input voltage is $V=40$ V. The switch is closed at $t=0$. Assume the circuit was at steady state before $t=0$. Find currents $i_2(t)$ and $i_3(t)$, together with $i_c(t)$ as the complete responses of the circuit for $t>0$. Make sure the signs of these currents are consistent with the assumed directions as shown in the figure.