Question

In the circuit shown aside the switch $S$ can be moved from $a$ to $b,$ connecting either inductance $L$ or capacitance $C$ to a resistor $R$.when the key is pressed the switch $S$ will be at either $a$ or $b$.In column $I,$ the variation of physical quantities charge,current,voltage etc.in time are given in terms of constants $C^{\prime }s$ and $K^{\prime }s$ the values of which depends on emf $V,R,L$ and $C$.In column $II,$ the physical quantities under different switch positions are given. the variation in column $I$ may correspond to one or more quantities of Column $II$.

Answer 1

Ans$:A\to 5,B\to 3,B\to 4,C\to 1,D\to 2$

Initially current $=0A$

After switch at $a$

$E=Ri+L\left(di/dt\right)$

so, Forced response is $i=\frac{E}{R}$

and Natural Response $i=A{e}^{-\left(\frac{R}{L}\right)t}$

$\Rightarrow i=\frac{E}{R}+A{e}^{(-\frac{R}{L})t}$
$V_L=L\frac{di}{dt}=-\left(\frac{R}{L}\right)A{e}^{(-\frac{R}{L})t}$

$\Rightarrow A\to 5$

Energy stored in inductor $=\frac{1}{2}L{I}^2$

$\Rightarrow D\to 2$

Voltage across the resistor $=iR=\frac{E}{R}+A{e}^{(-\frac{R}{L})t}$

$\Rightarrow B\to 3$

charge across the inductor $=$ integration of i w.r.t $t.$

$\Rightarrow C\to 1$