The circuit shown in the figure contains an inductor $L = 25 \text{ mH}$, a capacitor $C_0 = 10 \text{ } \mu\text{F}$, a resistor $R_0 = 5 \text{ } \Omega$ and an ideal battery of $20 \text{ V}$. The circuit also contains two keys $K_1$ and $K_2$. Initially, both the keys are open and there is no charge on the capacitor. At an instant, key $K_1$ is closed and immediately after this, the current in $R_0$ is found to be $I_1$. After a long time, the current attains a steady state value $I_2$. Thereafter, $K_2$ is closed and simultaneously $K_1$ is opened, and the voltage across $C_0$ oscillates with amplitude $V_0$ and angular frequency $\omega_0$. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.
$List-I$$List-II$
$(P)$ The value of $I_1$ in Ampere is$(1)$ $0$
$(Q)$ The value of $I_2$ in Ampere is$(2)$ $2$
$(R)$ The value of $\omega_0$ in kilo-radians/s is$(3)$ $4$
$(S)$ The value of $V_0$ in Volt is$(4)$ $20$
$(5)$ $200$

  • A
    $P \rightarrow 1; Q \rightarrow 3; R \rightarrow 2; S \rightarrow 5$
  • B
    $P \rightarrow 1; Q \rightarrow 2; R \rightarrow 3; S \rightarrow 5$
  • C
    $P \rightarrow 1; Q \rightarrow 3; R \rightarrow 2; S \rightarrow 4$
  • D
    $P \rightarrow 2; Q \rightarrow 5; R \rightarrow 3; S \rightarrow 4$

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$A$ thin conducting rod $MN$ of mass $20 \text{ g}$,length $25 \text{ cm}$ and resistance $10 \text{ }\Omega$ is held on frictionless,long,perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field $B_0 = 4 \text{ T}$ directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time $t = 0$ and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-$I$ with an appropriate value from List-$II$,and choose the correct option. [Given: The acceleration due to gravity $g = 10 \text{ m s}^{-2}$ and $e^{-1} = 0.4$]
List-$I$List-$II$
$(P)$ At $t = 0.2 \text{ s}$,the magnitude of the induced emf in Volt$(1)$ $0.07$
$(Q)$ At $t = 0.2 \text{ s}$,the magnitude of the magnetic force in Newton$(2)$ $0.144$
$(R)$ At $t = 0.2 \text{ s}$,the power dissipated as heat in Watt$(3)$ $1.20$
$(S)$ The magnitude of terminal velocity of the rod in $\text{m s}^{-1}$$(4)$ $0.12$
$(5)$ $2.00$

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The network shown in the figure is part of a complete circuit. If at a certain instant,the current $I$ is $5 \ A$ and it is decreasing at a rate of $10^3 \ A \ s^{-1}$,then $V_B - V_A$ equals.....$V$.

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The current $i$ in an inductance coil varies with time $t$ according to the following graph. Which of the following plots shows the variation of voltage $V$ in the coil?

$A$ semicircle conducting ring of radius $R$ is placed in the $xy$ plane,as shown in the figure. $A$ uniform magnetic field is set up along the $x$-axis. No $emf$ will be induced in the ring if:

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