Electromagnetic Induction Test

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Electromagnetic Induction Test - 56

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Weekly Quiz Competition

Question 1
1 / -0

The phenomena of a electromagnetic induction is

A
The process of charging a body

B
The process of generating magnetic field due to current passing through a coil

C
Producing induced current in a coil due to relative motion between a magnet and a coil

D
All the above
Question 2
1 / -0

When current flowing in a coil changes from $$3A$$ to $$2A$$ is one millisecond, $$5\ volt$$ emf is induced in it. The self-inductance of the coil will be

A
$$zero$$

B
$$5kh$$

C
$$5h$$

D
$$5\ mh$$

Solution

As we know,
$$EMF=L\times\dfrac{di}{dt}$$

$$5=L\times\dfrac{3-2}{0.001s}$$

$$L=\dfrac{5}{1000}$$

$$L=5mh$$
Question 3
1 / -0

The self induced e.m.f.in a 0.1 H coil when the current in it is changing at the rate of 200 ampere/second is

A
$$8\times 10^{-4}V$$

B
$$8\times 10^{-5}V$$

C
$$20 V$$

D
$$ 125 V$$

Solution

$$e = L\dfrac{di}{dt}$$

$$ \Rightarrow e = 0.1 \times 200 = 20 \,V$$
Question 4
1 / -0

A long solenoid of diameter $$0.1\ m$$ has $$2 \times {10^4}$$ turns per metre.At the centre of the solenoid, a coil of $$100$$ turns and radius $$0.01\ m$$ is placed with its axis coinciding with the solenoid axis.The current in the solenoid reduces at a constant rate to $$0\ A$$ from $$4\ A$$ in $$0.05\ s$$. If the resistance of the coil is $$10 \ {\pi ^2}\Omega ,$$ the total charge flowing through the coil during this time is.

A
$$32\ \pi \mu C$$

B
$$16\ \mu C$$

C
$$32\ \mu C$$

D
$$16\ \pi \mu C$$

Solution

Given,

Number of turns, $$n=100$$

Radius, $$r=0.01\,m$$

Resistance, $$R=10\pi^2 \Omega$$

As we know,

$$\epsilon=-N\dfrac{d\phi}{dt}$$

$$=\dfrac{\epsilon}{R}=-\dfrac NR\dfrac{d\phi}{dt}$$, $$\Delta I=-\dfrac NR\dfrac{d\phi}{dt}$$

$$\dfrac{\Delta}{\Delta t}=-\dfrac NR\dfrac{\Delta\phi}{\Delta t}\implies \Delta q=-[\dfrac NR(\dfrac{\Delta \phi}{\Delta t})]\Delta t$$

$$-$$ve sign shoes that induced emf opposes the change in flux.

$$\Delta q=\dfrac{\mu_0 ni\pi r^2}{R}$$

$$\Delta q=\dfrac{4\pi\times 10^{-7}\times 100\times 4\times \pi\times (0.01)^2}{10\pi^2}=32\mu C$$
Question 5
1 / -0

The coefficients of self induction of two inductance coils arc 0.0 1H and 0.03H respectively. When they are connected in series so as to support each other. then the resultant self inductance becomes 0.06 Henry. The value of coefficient of mutual induction will be-

A
0.02 H

B
0.05 H

C
0.01 H

D
ZERO

Solution

$$L1=0.01$$
$$L2=0.03$$
$$L eff =0.06$$
$$Leff = L1+L2+2M$$
$$0.06=0.01+0.03+2M$$
$$2M = 0.06-0.03$$
$$M=0.03/2$$
$$=0.015$$
Question 6
1 / -0

When a coil is connected to a D.C source of emf 12V,a current of 4 amp flows in it.If same coil is connected to 12V,50Hz AC source, the current is 2.4 A. The self inductance of the coil is (in henry)

A
$$\frac { 1 }{ 2\pi }$$

B
$$\frac { 1 }{ 10\pi }$$

C
$$\frac { 1 }{ 25\pi }$$

D
$$\frac { 1 }{ 5\pi }$$

Solution
Question 7
1 / -0

An average emf of $$20 V$$ is induced in an inductor when the current in it is changed from $$2.5 A$$ in one direction to the same value in the opposite direction in $$0.1$$ s. The self-inuctance of the inductor is

A
$$zero$$

B
$$0.2 H$$

C
$$0.4 H$$

D
$$1 H$$

Solution

Given that,

Average emf $$V=20V$$

Current $$i=2.5\,A$$

We know that,

$$ V=L\dfrac{dI}{dt} $$

$$ 20=L\times \dfrac{5}{0.1} $$

$$ L=\dfrac{20}{50} $$

$$ L=0.4\,Henry $$

Hence, the self-inductance is $$0.4\ henry$$
Question 8
1 / -0

A magnetic field $$\vec {B}=B_{0}\hat {k}$$ is present in elliptical region given by $$\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$$. If conducting rod of length $$2b (< 2a)$$ is kept parallel to $$y-$$axis, The rod starts moving with velocity $$v \hat {i}$$ and at $$t=0$$ centre of rod is at $$(-a, 0)$$. Find motional $$EMF$$ in rod as function of time $$t.t < \dfrac{2a}{v}$$.

A
$$2Bbv\sqrt{1-\dfrac{(vt-a)^{2}}{a^{2}}}$$

B
$$2bv^{2}\left[\dfrac{a^{2}t}{b^{3}}\right]$$

C
$$2Bav\sqrt{1-\dfrac{(vt-a)^{2}}{a^{2}}}$$

D
$$2Bbv$$
Question 9
1 / -0

An electron having kinetic energy T is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction $$\vec { \mathrm { B } }$$ If kinetic energy is doubled and magnetic induction tripled, the radius will

A
$$\frac { 3 R } { 2 }$$

B
$$ \frac{{\sqrt 2 }}{3}R$$

C
$$\sqrt { \frac { 2 } { 9 } } R$$

D
$$\sqrt { \frac { 4 } { 3 } } R$$

Solution

We know$$,$$
$$R = \frac{{\sqrt {2mk} }}{{qB}}$$
$$R' = \frac{{\sqrt {2m2k} }}{{q\left( {3B} \right)}}$$
$$ = \frac{{\sqrt 2 }}{3}\frac{{\sqrt {2mk} }}{{qB}}$$
$$ = \frac{{\sqrt 2 }}{3}R$$
Hence,
option $$(B)$$ is correct answer.
Question 10
1 / -0

In electromagnetic induction, The induced e.m.f in a coil is
in depended of

A
Change in flux

B
Resistance of coil

C
Time

D
None

Solution

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Electromagnetic Induction Test - 56

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Question 1

The process of charging a body

The process of generating magnetic field due to current passing through a coil

Producing induced current in a coil due to relative motion between a magnet and a coil

All the above

Question 2

$$zero$$

$$5kh$$

$$5h$$

$$5\ mh$$

Solution

Question 3

$$8\times 10^{-4}V$$

$$8\times 10^{-5}V$$

$$20 V$$

$$ 125 V$$

Solution

Question 4

$$32\ \pi \mu C$$

$$16\ \mu C$$

$$32\ \mu C$$

$$16\ \pi \mu C$$

Solution

Question 5

0.02 H

0.05 H

0.01 H

ZERO

Solution

Question 6

$$\frac { 1 }{ 2\pi }$$

$$\frac { 1 }{ 10\pi }$$

$$\frac { 1 }{ 25\pi }$$

$$\frac { 1 }{ 5\pi }$$

Solution

Question 7

$$zero$$

$$0.2 H$$

$$0.4 H$$

$$1 H$$

Solution

Question 8

$$2Bbv\sqrt{1-\dfrac{(vt-a)^{2}}{a^{2}}}$$

$$2bv^{2}\left[\dfrac{a^{2}t}{b^{3}}\right]$$

$$2Bav\sqrt{1-\dfrac{(vt-a)^{2}}{a^{2}}}$$

$$2Bbv$$

Question 9

$$\frac { 3 R } { 2 }$$

$$ \frac{{\sqrt 2 }}{3}R$$

$$\sqrt { \frac { 2 } { 9 } } R$$

$$\sqrt { \frac { 4 } { 3 } } R$$

Solution

Question 10

Change in flux

Resistance of coil

Time

None

Solution

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