Embibe Experts Solutions for Chapter: Electromagnetic Induction and Alternating Currents, Exercise 1: Exercise 1

A ring made of insulating material is rolling without slipping on a horizontal surface with a velocity of center of mass $V_0.$ A conducting wire of length $2R$ ( $R=$ radius of the ring) is fixed between two points of the circumference. At an instant, the wire is in a vertical position as shown in the figure. A uniform magnetic field, $B$ exists perpendicular to the plane of the ring. The magnitude of emf induced between the ends of the wire is, 

When the current in the portion of the circuit shown in the figure is $2 \mathrm{A}$ and increasing at the rate of $1 \mathrm{A} {\mathrm{s}}^{-1}$, the measured potential difference $V_{ab}=8 \mathrm{V}.$However, when the current is $2 \mathrm{A}$ and decreasing at the rate of $1 \mathrm{A} {\mathrm{s}}^{-1}$, the measured potential difference $V_{ab}=4 \mathrm{V}.$ The values of $R$ and $L$ are:

In an $LR$ circuit current at $t=0$ is $20 \mathrm{A}.$ After $2 \mathrm{s}$ it reduces to $18 \mathrm{A}$. The time constant of the circuit is (in second);

The magnetic field inside a long solenoid of cross-section $15 {\mathrm{cm}}^2$ is $200 \mathrm{T}$. This solenoid crosses a square coil of area $2 {\mathrm{m}}^2$ such that the length of the solenoid is parallel to the axis of coil. The magnetic flux linked through the square coil is $x \mathrm{Wb}$, then what is the value of $10x$?

A conducting rod $pq$ is sliding on two parallel conducting rods with constant velocity in a uniform magnetic field of induction $B=2 \mathrm{Wb} {\mathrm{m}}^{-2}$ as shown in the figure. The rods are connected with a circuit. What should be velocity of rod $pq$ (in $\mathrm{m} {\mathrm{s}}^{-1}$), if current in $2 \mathrm{\Omega }$ resistor is $0.1 \mathrm{A}?$

For a coil having $L=2 \mathrm{mH}$, current flows through it is $i=t^2{e}^{-t},$ then the time (in second) at which emf becomes zero is-

Power factor of an $L-R$ series circuit is $0.6$. and that of a $C-R$ series circuit is $0.5$. If the element ($L, C$ and $R$) of the two circuits are joined in series the power factor of this circuit is found to be $1$. The ratio of the resistance in the $L-R$ circuit to the resistance in the $C-R$ circuit is $\frac{\sqrt{x}}{4}$, find the value of $x$.

A series LCR circuit is designed to resonate at an angular frequency ${\omega }_0={10}^5 \mathrm{rad} {\mathrm{s}}^{-1}$. The circuit draws $16 \mathrm{W}$ power from $120 \mathrm{V}$ source at resonance. The value of resistance $R$ in the circuit is _____ $\mathrm{\Omega }$.