Tag: electromagnetic induction

Questions Related to electromagnetic induction

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

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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

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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

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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 $\dfrac{L _1}{L _2}=\dfrac{200*10^{-3}}{400*0.8*10^{-3}}=1/1.6$

Two concentric coils each of radius equal to $2\pi\ cm$ are placed at right angles to each other. $3$ Ampere and $4$ ampere are the currents flowing in each coil respectively. The magnetic induction in $Weber/m^{2}$ at the centre of the coils will be ($\mu _{0}=4\pi \times 10^{-7}\ Wb/A-m$)

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $12\times 10^{-5}$

  2. $10^{-5}$

  3. $5\times 10^{-5}$

  4. $7\times 10^{-5}$

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Correct Option: C
Explanation:
Magnetic Induction at centre of coil is
$B=\dfrac {\mu _0}{2r} \sqrt {I _1^2 +I _2^2}\quad I _1=3\ A$
$I _2=4\ A$
$=\dfrac {4\pi\times 10^{-7}}{2\times \dfrac {2\pi}{100}}\times \sqrt {3^2 +4^2}$
$=\dfrac {4\pi \times 10^{-5}\times 5}{2\times 2\pi}$
$=5\times 10^{-5} \dfrac {wb}{m^2}$

A 60 volt - 10 watt bulb is operated at 100 volt - 60 Hz a.c. The inductance required is?

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. 2.56 H

  2. 0.32 H

  3. 0.64 H

  4. 1.28 H

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Correct Option: D

Two coaxial coils are very close to each other and their mutual inductance is $5mH$. If a current $50sin{500t}$ is passed in one of the coils then the peak value of induced emf in the secondary coil will be

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. $5000V$

  2. $500V$

  3. $150V$

  4. $125V$

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Correct Option: D
Explanation:

According to principle of mutual inductance, flux induced in coil  is equa to the current flowing in coil 1

$\phi _{2}= Mi _{1}$
By Faraday's laws,
$\dfrac{d\phi _{2}}{dt}=M\dfrac{di _{1}}{dt}$ = EMF
$\therefore EMF = 5\times 10^{-3}\dfrac{d}{dt}50 sin 500t$
$\therefore EMF = 125 cos500t$
So, maximum vaue of EMF would be 125 V