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

We will write voltage drop equation as we go from A to B.\${ V }_{ A }-iR+V+L\dfrac { di }{ dt } ={ V }_{ B }\$\${ V }_{ A }-5\times 1+15-5\times { 10 }^{ -3 }\times (-{ 10 }^{ 3 })={ V }_{ B }\$\$V_B-V_A=15\$

Q: A pair of adjacent coil has a mutual inductance of \$1.5 \,H\$. If the current in one coil changes from \$0\$ to \$20 \,A\$ in \$0.5\$ sec, what is the change of flux linkage with the other coil?

We know that \$e=\dfrac{d\phi }{dt}=M\dfrac{di}{dt}\$Therefore, \$d\phi =M{di}=1.5\times (20-0)=30Wb\$

Question 1

Derive the expression for motional EMF induced in a conductor moving in a uniform magnetic field.

Accepted Answer

Let  us  consider  a  straight  conductor  moving  in  a  uniform  and  time-independent magnetic field.  The figure  shows a rectangular wire PQRS in which the conductor PQ is free to move.  Rod PQ is moved towards the left with a constant velocity v.PQRS forms closed circuit enclosing an area that changes as PQ moves. It is placed in a uniform magnetic field B perpendicular to the plane of our system. Let the length RQ =x and RS =l, the magnetic flux $\phi_B$ enclosed  by the loop PQRS $\phi_B=Blx$As&#10; x is changing with time, the rate of change of flux $\phi_B$ will &#10;induce an emf given according to Faraday's law of electromagnetic &#10;induction  : $\epsilon=-\frac{d\phi_B}{dt}=-\frac{d}{dt} (Blx)=-Blv$This induced emf Blv is motional emf.

Question 2

A coil of insulated copper wire is connected to a galvanometer. What will happen if a bar magnet is (i) pushed into the coil (ii) withdrawn from inside the coil (iii) held stationary inside the coil.

Accepted Answer

When a coil of insulated copper wire is connected to a galvanometer, following observations will take place for each option:(I) If a bar magnet is pushed into the coil, an electric current will be induced in coil due to electromagnetic induction.(ii) If a bar magnet is withdrawn from inside, again current will be induced in the copper wire due to electromagnetic induction but this time the direction of current will be reverse in galvanometer.(iii) If a  bar magnet is held stationary inside the coil then no current is induced and therefore there is no deflection in the galvanometer.

Question 3

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

Accepted Answer

We will write voltage drop equation as we go from A to B.${ V }_{ A }-iR+V+L\dfrac { di }{ dt } ={ V }_{ B }$${ V }_{ A }-5\times 1+15-5\times { 10 }^{ -3 }\times (-{ 10 }^{ 3 })={ V }_{ B }$$V_B-V_A=15$

Question 4

In the arrangement shown in the figure, there are two coils wound on a non-conducting cylindrical rod. Initially, the key is not inserted. Then the key is inserted and later removed. Then :

Accepted Answer

In the figure, two coils are not electrically connected to each other because they are wound on a non conducting rod. Say Coil-1 is connected across a battery through a key. This coil is called primary coil. Coil-2 is connected across a galvanometer. This coil is called secondary coil. When the key is pressed it is observed that, the galvanometer shows a small momentary deflection and then returns to zero. When the key is released, the galvanometer again shows a small momentary deflection, but in opposite direction and then returns to zero. As the coil is connected to a non-conducting rod the self induced electromotive force or voltage is very less and thus the current that flows in one direction slowly diminishes and returns to zero. Similarly when the key is released the current flows in the opposite direction and slowly diminishes.Thus, the rate of change of electromotive force (e.m.f.) in coil-1, decides the magnitude of deflection of galvanometer. The magnetic flux of primary coil is linked through the rod to the secondary coil. Thus, the induced e.m.f. or current is produced in a coil when varying current flows through a neighboring coil.

Question 5

Lenz's law is a consequence of law of conservation of

Accepted Answer

Lenz's law is based upon the law of conservation of energy. Lenz law states that the induced current always tends to oppose the &#10;cause which produce it. So in order to do work against opposing force we &#10;have to put extra effort. This extra work leads to periodic change in &#10;magnetic flux hence more current is induced. Thus the extra effort is &#10;just transformed into electrical energy which is law of conservation of &#10;energy.

Question 6

A pair of adjacent coil has a mutual inductance of $1.5 \,H$. If the current in one coil changes from $0$ to $20 \,A$  in $0.5$ sec, what is the change of flux linkage with the other coil?

Accepted Answer

We know that $e=\dfrac{d\phi }{dt}=M\dfrac{di}{dt}$Therefore, $d\phi  =M{di}=1.5\times (20-0)=30Wb$

Question 7

Two circular coils A and B are placed close to each other . If the current in the coil A is changed, some current be induced in the coil B. Give reason.

Accepted Answer

When two circular coils A and B are placed close to each other, and the current in the coil A is changed then some current will be induced in the coil B and the magnetic field associated with it also changes. Thus the magnetic field around coil B also changes. This change in the magnetic field lines around coil B induces an electric current in it. This process is known as electromagnetic induction.

Question 8

State Faraday's law of electromagnetic induction.

Accepted Answer

Faraday's law of electromagnetic induction:When a changing magnetic field is linked with a coil, an emf is induced in it. This change in magnetic field may be caused by changing the magnetic field strength by moving a magnet towards or away from the coil, or moving the coil into or out of the magnetic field as desired. Or in simple words, we can say that the magnitude of the emf induced in the circuit is proportional to the rate of change of flux.The Faraday's law of electromagnetic induction says that the E.M.F. induced in a coil '$e$' $= -$ (rate of change of magnetic flux linkage) where,the Flux linkage $=$ number  of  turns 'N' times magnetic field 'B' $\times$ area 'A' $\times \cos\theta$where,$\theta$ is the angle between magnetic field B and area A.$\theta$ at any instant $'t'=$(angular  velocity '$w$')$\times$ (time  instant '$t$'). That is, $\theta$ $=w\times t$.E.M.F. induced in a coil '$e$'$=N\times B\times A\times w\times \sin w\times t$.

Question 9

What is eddy current? Mention two applications of eddy current.

Accepted Answer

Eddy currents are the currents induced in a metallic plate when it is kept in a time varying magnetic field. Magnetic flux linked with the plate changes and so the induced current is set up. Eddy currents are sometimes so strong, that metallic plate become red hot.Application:-(1)-In induction furnace, the metal to be heated is placed in rapidly varying magnetic field produced by high frequency alternating current. Strong eddy currents are set up in the metal produce so much heat that the metal melts. This process is used in extracting a metal from its ore.The arrangement of heating the metal by means of strong induced current is called the induction furnace.(2)-Induction motor, the eddy currents may be used to rotate the rotor. When a metallic cylinder(or rotor) is placed in a rotating magnetic field , eddy currents are produced in it. According to Lenz's law, these currents tends to reduce to relative motion between the cylinder and the field. The cylinder, therefore, begins to rotate in the direction in the field. This is the principle of induction motion.

Question 10

The phenomenon of electromagnetic induction is :

Accepted Answer

Hint: When there is a change in the magnetic flux through a closed loop, an induced current is generated in such a way that it tries to oppose the change in the flux$\textbf{Step 1: Discussing the electromagnetic induction}$$\bullet$Electromagnetic induction is a phenomenon in which an emf is generated if there is a change in the magnetic flux through a closed-loop. $\bullet$When there is relative motion between a magnet and the coil, magnetic flux changes, and hence an electromotive force is generated in the coil. This electromotive force generates induced current.$\textbf{Therefore, option (C) is the correct answer.}$