A constant current source is supplying $$10A$$ to a circuit shown in Fig. the switch $$S,$$ which is initially closed for a sufficiently long time, is suddenly opened. Obtain the differential equation governing the behaviour of the inductor current and hence obtain the complete time response of the inductor current. What is the energy stored in $$L,$$ a long time after the switch is opened?

In the given circuit, the capacitor is initially charged to $$12$$ $$V. $$ Find the mathematical expression for the voltage across the capacitor $${{V_C}}$$ after closing the switch at $$t = 0.$$

The switch in the following circuit, shown in Fig. has been connected to the $$12V$$ source for a long time. At $$t=0,$$ the switch is thrown to $$24$$ $$V$$.

$$L = 2\,H,\,\,{R_1} = 10\,\Omega ,\,\,{R_2} = 2\,\Omega ,\,\,C = 0.25\,\mu F$$
$$(a)$$ Determine $${i_L}\left( 0 \right)$$ and $${V_C}\left( 0 \right)$$
$$(b)$$ Write the differential equation governing $${V_C}\left( t \right)$$ for $$t>0$$
$$(c)$$ Compute the steady state value of $${V_C}\left( t \right)$$

In the circuit shown in Fig., $${e_g}\left( t \right) = 2.5t$$ volts. What are the values of $$i(t)$$ and $${V_L}\left( t \right)$$ at $$t=4$$ seconds?