Electromagnetic Induction Test

Result

Electromagnetic Induction Test - 26

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Question 1
1 / -0

Two coils of self inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:

A
10 mH

B
6 mH

C
4 mH

D
16 mH

Solution

Given,
$$L_1=2mH$$
$$L_2=8mH$$
The mutual inductance between coil is
$$M=\sqrt{L_1L_2}$$
$$M=\sqrt{2\times 8}=\sqrt{16}mH$$
$$M=4mH$$
The correct option is C.
Question 2
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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 $$(\varepsilon)$$in the coil with time

A

B

C

D

Solution
Question 3
1 / -0

A long straight wire is placed along the axis of a circular ring of radius R. The mutual inductance of this system is

A
$$\frac{\mu _{0}R}{2}$$

B
$$\frac{\mu _{0}\pi R}{2}$$

C
$$\frac{\mu _{0}}{2}$$

D
$$0$$

Solution

Magnetic field due to wire at the ring is
$$\begin{array}{l} B=\frac { { \mu oi } }{ { 4\pi R } } ,\therefore then\, \, \emptyset = \\ \emptyset =\overrightarrow { B } .\overrightarrow { A } \Rightarrow \left| B \right| \left| A \right| \cos \theta \\ \theta =90^{ \circ } \\ \emptyset =O,as\cos 90^{ \circ }=0 \\ \therefore mutual\, \, induction=0 \end{array}$$
Question 4
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Magnetic flux $$\phi$$ (in weber) linked with a closed circuit of resistance $$10 \Omega$$ varies with time t (in second) as $$\phi = 5{t^2} - 4t + 1$$. The induced electromotive force in the circuit at t = 0.2 second is

A
0.4 V

B
-0.4 V

C
-2.0 V

D
2.0 V

Solution

ϕ=BA
Question 5
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Refer to the figure. When does the the galvanometer (G) deflect ?

A
The magnet is pushed into the coil

B
The magnet is rotated into the coil

C
The magnet is stationary at the centre of the coil.

D
The number of turns in the coil is reduced.

Solution

The deflection in the galvanometer (G) occurs, when the magnet is pushed into the coil. This is because the relative motion between the two induces an emf into the coil.
Question 6
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A conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An emf is induced in the loop if

A
it is translated

B
it is rotated about its axis

C
it is kept untouched for several minutes

D
it is cut into two pieces

Solution

e.m.f is induced in the coil when the flux linked with the coil changes.

And magnetic flux=$$\phi=\vec{B}.\vec{A}=BA\cos{\theta}$$ where=$$\vec{A}$$=area vector of coil
and $$\theta$$=angle between $$\vec{A}$$ and $$\vec{B}$$

Hence, on changing $$\theta$$, emf can be induced.

Answer-(B).
Question 7
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The induced emf produced when a magnet is inserted into a coil does not depend upon:

A
The number of turns in the coil

B
The resistance of the coil

C
The speed of approach of the magnet

D
All the above

Solution

The induced emf produced when a magnet is inserted into a coil does not depend upon the resistance of the coil.
Question 8
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Whenever current is changed in a coil, an induced e.m.f. is produced in the same coil, This property of the coil is due to

A
mutual induction

B
self induction

C
eddy currents

D
hysteresis

Solution

The property of induction of e.m.f. in the same coil when there is a change in current in it is called $$self\hspace{2mm}induction.$$

Hence, answer is option-(B).
Question 9
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Whenever the magnetic flux linked with a coil changes, an
induced e.m.f. is produced in the circuit. The e.m.f. lasts

A
for a short time

B
for a long time

C
for ever

D
so long as the change in flux takes place

Solution

The induced emf ,$$E=-\dfrac{d\phi}{dt}$$ where $$\phi$$=magnetic flux

Hence, emf will last as long as flux keeps changing.

Hence, answer is option-(D).
Question 10
1 / -0

To obtain maximum EMF from a number of cells, they must be connected in

A
Series

B
Parallel

C
Both (a) and (b) above

D
None of these

Solution

A. Series
Cells in Series connection.
In series, cells are joined end to end so that the same current flows through each cell. In case if the cells are connected in series the emf of the battery connected to the sum of the emf of the individual cell,
If E is the overall emf of the battery combined with n number cells and E1, E2,......Em is the EMFs of individual cell
Then E= E1+E2+...............+Em.