Tag: electromagnetic induction and alternating currents

Quizzes (10) Questions (183)

Questions Related to electromagnetic induction and alternating currents

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

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:

  1. 10 mH

  2. 6 mH

  3. 4 mH

  4. 16 mH
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A circular copper disc 10 cm in diameter rotates at 1800 revolution per minute about an axis through its centre and at right angles to disc. A uniform field of induction B of 1 Wb $m^2$ is perpendicular to disc. What potential difference is developed between the axis of the disc and the rim ?

  1. 0.023 V

  2. 0.23 V

  3. 23 V

  4. 230 V
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here, 

$l = r = 5\, cm = 5 \times 10^{-2} m,$
B = 1 Wb $m^{-2}$

$ \omega = 2 \pi \left( \dfrac{1800}{60} \right) \, rad \, s^{-1} = 60 \pi \, rad \, s^{-1},$

$\epsilon \, = \, \dfrac{1}{2} Bl^2 \omega \, =\, \dfrac{1}{2} \times 1 \times (5 \times 10^{-2})^2 \times 60 \pi = 0.23 V$

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

If the self inductance of 500 turns coil is 125 mH, then the self inductance of the similar coil of 800 mH

  1. 48.8 mH

  2. 200 mH

  3. 290 mH

  4. 320 mH
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$L=\mu _o \mu _r N^2Al$
For similar coil, $A, l$ will be same 
So,   $ \, \dfrac{L _1}{L _2} = \dfrac{N _1^2}{N _2^2}$

$ L _{800}= \dfrac{N _{800} ^2}{N _{500}^2}\times L _{500}= \, \dfrac{125}{(500)^2} \, \times \, (800)^2 \, = \, 320 \, mH$

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

The mutual inductance $M _{12}$ of a coil 1 with respect to coil 2

  1. increases when they are brought nearer

  2. depends on the current passing through the coils.

  3. increases when one of them is rotated about an axis.

  4. both (a) and (b) are correct
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mutual Induction: Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighbouring coil or circuit will also change. Hence an emf will be induced in the neighbouring coil or circuit. This phenomenon is called ‘mutual induction’.


If the two coils $1$ and $2$ are present with mutual inductance $M _1$ and $M _2$. Then the mutual inductance of the coil 1 due to 2 increases when they are bought near since, mutual inductance is  proportional to the flux passed through the coil.

The mutual induction of $M _{12}$ is same as $M _{21}$

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Match the following:

Quantity Formula
1) Magnetic flux linked with a coil a) $\displaystyle -N\frac { d\phi  }{ dt } $
2) Induced emf b) $\displaystyle { \mu  } _{ r }{ \mu  } _{ 0 }{ n } _{ 1 }{ n } _{ 2 }{ \pi r } _{ 1 }^{ 2 }l$
3) Force on a charged particle moving in a electric and magnetic field c) $\displaystyle BA\cos { \theta  } $
4) Mutual inductance of a solenoid d) $\displaystyle q\left( \overline { E } +\overline { v } \times \overline { B }  \right) $

  1. 1-c, 2-d, 3-b, 4-a

  2. 1-c, 2-a, 3-d, 4-b

  3. 1-b, 2-a, 3-c, 4-d

  4. 1-a, 2-b, 3-d, 4-c
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

1) Magnetic flux through any area is the scalar product of its area vector with the magnetic field vector. Thus for a coil, it is $\vec{B}.\vec{A}=BAcos\theta$

2) Emf induced in a coil due to changing flux through it is given by Faraday's Law,
$Emf = -N\dfrac{d\phi}{dt}$
3) Force on a charged particle due to electric field = $q\vec{E}$
Force on a moving charged particle due to magnetic field = $q(\vec{v}\times \vec{B})$
Thus, force on a moving charged particle in an electric and magnetic field = $q(\vec{E}+\vec{v}\times \vec{B})$
4) Mutual inductance of a solenoid is found out to be : $\mu _r\mu _0n _1n _2\pi r _1^2l$

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

In the method using the transformers, assume that the ratio of the number of turns in the primary to that in secondary in the step-up transformer is $1:10$. If the power to the consumer has to be supplied at $200\ V$, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is:

  1. $200:1$
  2. $150:1$
  3. $100:1$
  4. $50:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

 An inductor of inductance $100\ mH$ is connected in series with a resistance, a variable capacitance and an AC source of frequency $2.0\ kHz$; The value of the capacitance so that maximum current may be drawn into the circuit. 

  1. 50 nF

  2. 60 nF

  3. 63 nF

  4. 79 nF
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l}{X _L} = Lw = {10^{ - 1}} \times 2\pi  \times 2 \times {10^3}\{X _L} = 4\pi  \times {10^2}\Z = \sqrt {{{\left( {{X _L} - {X _C}} \right)}^2} + {R^2}} \i = \dfrac{V}{Z} = \dfrac{V}{{\sqrt {{{\left( {{X _L} - {X _C}} \right)}^2} + {R^2}} }}\for,{i _{\max }}\{X _L} = {X _C}\\therefore {X _C} = Lw = \dfrac{1}{{Cw}}\C = \dfrac{1}{{{w^2}L}} = \dfrac{1}{{{{10}^{ - 1}} \times 4{\pi ^2} \times 4 \times {{10}^6}}}\ = \dfrac{{{{10}^{ - 5}}}}{{16{\pi ^2}}} = 63nF\end{array}$

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

$5 \mathrm { mV }$ is induced in a coil, when current in another nearby coil changes by $5 \mathrm { A }$ in $0.1$sec. The mutual inductance between the two coils will be

  1. $0.1 \mathrm { H }$
  2. $0.2 \mathrm { H }$
  3. $0.1 \mathrm { mH }$
  4. $0.2 \mathrm { mH }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The induced emf is given by e = M * (di / dt). Rearranging for mutual inductance M gives M = e / (di / dt). Substituting e = 5 mV = 5 x 10^-3 V and di/dt = 5 A / 0.1 s = 50 A/s yields M = (5 x 10^-3) / 50 = 0.1 x 10^-3 H = 0.1 mH.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

In mutual induction 
A: when current in one coil increases, induced current in neighbouring coil flows in the opposite direction
B: When current in one coil decreases, induced current in neighbouring coil flows in the opposite direction

  1. A is true, B is false

  2. A and B are false

  3. A and B are true

  4. A is false, B is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lenz's Law states that the induced current will flow in a direction that opposes the change in magnetic flux. If current in the primary coil increases, the induced current in the secondary coil creates a magnetic field opposing the increase (opposite direction). If current decreases, the induced current creates a field to support the flux (same direction). Thus, A is true and B is false.