Electromagnetic Induction Test

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Electromagnetic Induction Test - 62

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Question 1
1 / -0

The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is $$10 \Omega$$. The current in the circuit will be now

A
$$i = 0.5 \,A$$

B
$$i > 0.5 \,A$$

C
$$i < 0.5 \,A$$

D
$$i = 0$$

Solution

If resistance is constant $$(10\Omega)$$ then steady current in the circuit $$i = \dfrac{5}{10} = 0.5 \,A.$$ But resistance is increasing it means current through the circuit start decreasing. Hence inductance comes in picture which induces a current in the circuit in the same direction of main current.So $$i > 0.5 \,A.$$
Question 2
1 / -0

The current through a $$4.6\, H$$ inductor is shown in the following graph. The induced emf during the time interval $$t = 5$$ milli-sec to $$6$$ milli-sec will be

A
$$10 \,V$$

B
$$-23 \times 10^3 \,V$$

C
$$23 \times 10^3 \,V$$

D
Zero

Solution

Rate of decay of current between $$t = 5$$ ms to $$6$$ ms
$$= \dfrac{di}{dt} = -$$ (Slope of the line BC)
$$= - \left ( \dfrac{5}{1 \times 10^{-3}} \right ) = -5 \times 10^3 \,A / s.$$

Hence induced emf
$$e = -L \dfrac{di}{dt} = -4.6 \times (-5 \times 10^3) = 23 \times 10^3 \,V.$$
Question 3
1 / -0

A horizontal loop abcd is moved across the pole pieces of a magnet as shown in fig. with a constant speed v. When the edge ab of the loop enters the pole pieces at time $$t = 0$$ sec. Which one of the following graphs represents correctly the induced emf in the coil

A

B

C

D

Solution

When loop enters in field between the pole pieces, flux linked with the coil first increases (constantly) so a constant emf induces, when coil entered completely within the field, no flux change so $$e = 0.$$
When coil exit out, flux linked with the coil decreases, hence again emf induces, but in opposite direction.
Question 4
1 / -0

For previous objective, which of the following graphs is correct

A

B

C

D

Solution

If at any instant, current through the circuit is i then applying Kirchoffs voltage law, $$iR + e = E \Rightarrow e = E - iR.$$ Therefore,graph between e and i will be a straight line having negative slope and having a positive intercept.
Question 5
1 / -0

The magnetic induction at any point due to a long straight wire carrying a current is

A
Proportional to the distance from the wire

B
Inversely proportional to the distance from wire

C
Inversely proportional proportional to the square of the distance from the wire

D
Does not depend on distance

Solution

Magnetic induction is given by
$$B=\dfrac{\mu_0 i}{2\pi r}$$
So, $$B \propto \dfrac 1r$$
Question 6
1 / -0

If 1 A of current is passed through CuSO $$_{4}$$ solution for 10 seconds,then the number of copper ions deposited at the cathode will be about

A
$$1.6\times10 ^{19}$$

B
$$3.1\times10 ^{19}$$

C
$$4.8\times10 ^{19}$$

D
$$6.2\times10 ^{19}$$

Solution

1A of current is passed through the solution for 10 seconds .
Then the total charge supplied $$1\times 10=10C\therefore 2$$ electronic charge $$(3.2\times 10^{-19}C)$$ liberates one $$Cu^{++}$$ $$\therefore $$ Number of $$Cu^{++}$$ ions liberates by 10 C charge $$=\dfrac{1}{3.2\times 10^{-19}}\times 10=3.1\times 10^{19}$$
Question 7
1 / -0

The device that does not work on the principle of mutual induction is

A
Induction coil

B
Motor

C
Tesla coil

D
Transformer

Solution
Question 8
1 / -0

In the following figure, the magnet is moved towards the coil with a speed v and induced emf is e. If magnet and coil recede away from one another each moving with speed v, the induced emf in the coil will be

A
$$e$$

B
$$2e$$

C
$$e / 2$$

D
$$4e$$

Solution

$$\left ( \dfrac{d\phi}{dt}\right)_{In \,first \,case} = e$$

Magnet and coil recede away from one another each moving with speed v, Hence relative velocity $$V_r=2V$$

$$\left ( \dfrac{d\phi}{dt} \right )_{relative \,velocity 2v} = 2 \left ( \dfrac{d\phi}{dt} \right )_{1 case} = 2e$$
Question 9
1 / -0

If a conducting rod moves with a constant velocity $$ v $$ in a magnetic field, emf is induced between both its ends if:

A
$$ v $$ and $$ B $$ are parallel

B
$$ v $$ is perpendicular to $$ \overrightarrow{B} $$

C
$$ v$$ and $$ B $$ are in opposite direction

D
All of the above

Solution

The emf will only be induced if $$ v $$ is perpendicular to $$ \overrightarrow{B} $$
Velocity $$(\overrightarrow{v})$$ is perpendicular to magnetic field $$(\overrightarrow{B})$$
Question 10
1 / -0

What would be the coefficient of self-inductance of a coil $$ 100 turns, $$ if $$ 5 A $$ current flows through it? The magnetic flux is of $$ 5 \times 10^{3} $$ Maxwell.

A
$$ 0.5 \times 10^{-3} H $$

B
$$ 2 \times 10^{-3} H $$

C
$$ Zero $$

D
$$ 10^{-3}H $$

Solution

Given, $$ N=100, I=5 amp$$
$$\phi_B=5 \times 10^{3} Mx $$
=$$ 5 \times 10^3 \times 10^{-8} wb $$

coefficient of self induction
$$ L=-\dfrac{N \phi_B}{I}$$

$$=-\dfrac{100\times 5\times 10^{-5}}{(0-5)}$$
$$=10^{-3} H $$