$A$ flat coil of $500$ turns,each of area $50 \,cm^2$,rotates in a uniform magnetic field of $0.14 \,Wb/m^2$ about an axis normal to the field at an angular speed of $150 \,rad/s$. The coil has a resistance of $5 \,\Omega$. The induced $e.m.f.$ is applied to an external resistance of $10 \,\Omega$. The peak current through the resistance is .......... $A$. (in $.5$)

The current $i$ in an induction coil varies with time $t$ according to the graph shown in the figure. Which of the following graphs shows the induced emf $(E)$ in the coil with time?

$A$ circular coil of $500$ turns of wire has an enclosed area of $0.1\,m^2$ per turn. It is kept perpendicular to a magnetic field of induction $0.2\,T$ and rotated by $180^o$ about a diameter perpendicular to the field in $0.1\,s$. How much charge will pass when the coil is connected to a galvanometer with a combined resistance of $50\,\Omega$?

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	$(4)$ $20$
	$(5)$ $200$

$A$ triangular wire frame (each side $= 2 \, m$) is placed in a region of time-variant magnetic field having $dB/dt = \sqrt{3} \, T/s$. The magnetic field is perpendicular to the plane of the triangle. The base of the triangle $AB$ has a resistance $1 \, \Omega$ while the other two sides have resistance $2 \, \Omega$ each. The magnitude of potential difference between the points $A$ and $B$ will be....$V$

The current $(I)$ in the inductance is varying with time according to the plot shown in the figure. Which one of the following is the correct variation of voltage $(V)$ with time in the coil?