Tag: physics

Questions Related to physics

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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 48.8 mH

  2. 200 mH

  3. 290 mH

  4. 320 mH

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Correct Option: D
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$

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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  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

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Correct Option: A
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 $M _{21}$

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) $
mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  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

Show answer
Correct Option: B
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 : $\mu _r\mu _0n _1n _2\pi r _1^2l$

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:

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $200:1$

  2. $150:1$

  3. $100:1$

  4. $50:1$

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Correct Option: A

 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. 

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 50 nF

  2. 60 nF

  3. 63 nF

  4. 79 nF

Show answer
Correct Option: C
Explanation:

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

$5 \mathrm { mV }$ 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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $0.1 \mathrm { H }$

  2. $0.2 \mathrm { H }$

  3. $0.1 \mathrm { mH }$

  4. $0.2 \mathrm { mH }$

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Correct Option: A

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

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  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

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Correct Option: A

In case of all flux from the current  in coil 1 links with coil 2, the coefficient of coupling will be

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 2.0

  2. 1.0

  3. 0.5

  4. zero

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Correct Option: B
Explanation:

If all flux from the current in coil 1 links with coil 2, then that is referred as an ideal transformer. For an ideal transformer, the coefficient coupling is 1.

The induction coil works on the principle of.

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. Self-induction

  2. Mutual induction

  3. Ampere's rule

  4. Fleming's right hand rule

Show answer
Correct Option: B
Explanation:

Induction coil works on the principle of mutual induction that an emf or current is induced in the second coil if the magnetic flux due to first coil linked with the second coil changes.

Two coils A and B have 200 and 400 turns respectively. A current of 1 A in coil A causes a flux per turn of $10^{-3}$ Wb to link with A and a flux per turn of $0.8 \times 10^{-3}$ Wb through B. The ratio of self-inductance of A and the mutual inductance of A and B is :

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 5/4

  2. 1/1.6

  3. 1.6

  4. 1

Show answer
Correct Option: B
Explanation:

Two coils A and B have 200 and 400 turns respectively. A current of 1 A in coil A causes a flux per turn of 10−3 Wb to link with A and a flux per turn of 0.8×10−3 Wb through B. The ratio of self-inductance of A and the mutual inductance of A and B is $\dfrac{L _1}{L _2}=\dfrac{200*10^{-3}}{400*0.8*10^{-3}}=1/1.6$