Tag: electromagnetic induction

Questions Related to electromagnetic induction

The time constant of a circuit is 10 sec, When a resistance of $ 100 \Omega $ is connected in series in a previous circuit then time constant becomes 2 second,then the self inductance of the circuit is;-

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $250 H$

  2. $50H$

  3. $150 H$

  4. $25 H$

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Correct Option: A
Explanation:

In LR circuit,

The time constant $\tau=\dfrac{L}{R}$
$10=\dfrac{L}{R}$
$L=10R$. . . . . . .(1)
When Resistance $100\Omega $ is connect in series, than the time constant is
$\tau'=\dfrac{L}{R+100}=2s$
$L=2R+200$. . . . . . .(2)
Equating equation (1 ) and (2), we get
$2R+200=10R$
$8R=200$
$R=25\Omega$
From equation (1),
$L=10R=10\times 25$
$L=250H$

the number of turn of primary and secondary coil of the transformer is 5 and 10 respectively ad the mutual inductance is 25 H. if the number f turns of the primary and secondary is made 10 and 5 , then the mutual inductance of the coils will be

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. 6.25 H

  2. 12.5 H

  3. 25 H

  4. 50 H

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Correct Option: D
Explanation:

$M=\mu _o\mu _r \cfrac {N _1N _2}{l}A$

$M \propto N _1N _2$
Since $N _1N _2=10 \times 5= 5 \times 10=50$ in both cases.
Mutual inductance will remain same.

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-

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. 0.02 H

  2. 0.05 H

  3. 0.01 H

  4. ZERO

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Correct Option: C
Explanation:

$L1=0.01$

$L2=0.03$
$L eff =0.06$

$Leff = L1+L2+2M$
$0.06=0.01+0.03+2M$
$2M = 0.06-0.03$
$M=0.03/2$
$=0.015$

In an induction coil, the coefficient of mutual induction is 4 henry. If a current of 5 ampere in 1  the primary coil is cut off in $\frac { 1 }{ 1500 } $s, the e.m.f at the terminals of the secondary coil will be:

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. 15 kV

  2. 60 kV

  3. 10 kV

  4. 30 kV

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Correct Option: D
Explanation:

${\phi _{21}} = M.i,$

$ \Rightarrow v = \frac{{d{\phi _{21}}}}{{dt}} = M\frac{{di}}{{dt}}$
$ = 4 \times \frac{5}{{\left( {1/1500} \right)}}$
$ = 20 \times 1500$
$ = 30kv$
Hence,
option $(D)$ is correct answer.

The inductance is measured in 

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. Ohm

  2. Farad

  3. henery

  4. None of these

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Correct Option: C

if the length and area of cross section of an inductor remain same but the number of turns is doubled its self inductance will become:

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. half

  2. four time

  3. double

  4. one- fourth

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Correct Option: B

The SI unit of inductance, the henry, can be written as :

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. weber / ampere

  2. volt second / ampere

  3. joule / ampere$^2$

  4. ohm second

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Correct Option: A,B,C,D
Explanation:

$ L\dfrac{dI}{dt} = emf = \dfrac{d\phi}{dt}$


a) $ [L] = weber / ampere $

b) $ [L] = volt.second / ampere $

c) $ Joule = volt \times ampere \times second $

$ \Rightarrow volt \times second = Joule / ampere$

$ \Rightarrow [L] = joule/ ampere^2$

d) $ V = IR \Rightarrow volt = ampere.ohm$

$\Rightarrow [L] = ohm.second$.

If a spark is produced on removing the load from an AC circuit then the element connected in the circuit is

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. high resistance

  2. high capacitance

  3. high inductance

  4. high impedance

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Correct Option: C
Explanation:

On removal of load from the circuit, the circuit suddenly becomes an open circuit.
Thus $ \dfrac{di}{dt} \rightarrow \infty $
For sparking, high voltage must appear across the open ends. This will happen only in case of an inductor as the voltage drop across the inductor is $ L\dfrac{di}{dt} $
Therefore, the circuit has high inductance.

If N is the number of turns in a coil, the value of self-inductance varies are

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. N$^o$

  2. N

  3. N$^2$

  4. N$^{-2}$

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Correct Option: C
Explanation:

Factual question, self inductance is proportional to square of the number of turns in coil.

Which of the following units denotes the dimensions ${M}{L}^{2}/{Q}^{2}$, where ${Q}$ denotes the electric charge?

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $Weber$ ($Wb$)

  2. $Wb$$/\mathrm{m}^{2}$

  3. $Henry$ ($H$)

  4. $\mathrm{H}/\mathrm{m}^{2}$

Show answer
Correct Option: C
Explanation:

Weber $=ML^2T^{-2}I^{-1}$
$=ML^2T^{-2}Q^{-1}T=ML^2T^{-1}Q^{-1}$   ($I=QT^{-1}$)
Henry H is  SI unit of inductance. 
$H=ML^2T^{-2}I^{-2}$     also $I=QT^{-1}$
so $H=ML^2T^{-2}Q^{-2}T^2=ML^2Q^{-2}$