Tag: introduction to induction

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Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

If circular coil with $N _{1}$ turns is changed in to a coil of $N _{2}$ turns. What will be the ratio of self inductances in both cases.

  1. $\dfrac {N _{1}}{N _{2}}$
  2. $\dfrac {N _{2}}{N _{1}}$
  3. $\dfrac {N _{1}^{2}}{N _{2}^{2}}$
  4. $\sqrt {\dfrac {N _{1}}{N _{2}}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If circular coil with N1 turns is changed in to a coil of N2 turns. 

$L=\dfrac{Nd \phi}{dt} $
$L _1=\dfrac{N _1d \phi}{dt} $
$L _2=\dfrac{N _2d \phi}{dt} $ 
 L is in Henries
        N is the Number of Turns
        Φ is the Magnetic Flux
        Ι  is in Amperes
$\dfrac{L _1}{L _2}=\dfrac{N _1}{N _2} $
Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

If the number of turns per unit length of a coil of a solenoid is doubled the self-inductance of the solenoid will:

  1. remain unchanged

  2. be halved

  3. be doubled

  4. become four times
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The self-inductance of a solenoid is proportional to the square of the number of turns per unit length (L is proportional to n^2). If n is doubled, L becomes 2^2 = 4 times the original value.

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

Henry, the SI unit of inductance can be written as :

  1. weber ampere$^{-1}$
  2. volt second ampere$^{-1}$
  3. joule ampere$^{-1}$
  4. ohm s$^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The SI unit of inductance is Henry,
$\displaystyle L =-\dfrac{e}{\dfrac{di}{dt}}$
SI unit $= \displaystyle \dfrac{volt}{A} \times s$
$=volt \times second \times  ampere^{-1}$

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

Multiple Correct Answers Type
The SI unit of inductance, henry, can be written as

  1. Weber/ampere

  2. Volt-second / ampere
  3. $Joule / (ampere)^2$

  4. Ohm-second
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

$L=\cfrac{\phi}{i}$

$L=\cfrac{weber}{Ampere}$
$V=L\cfrac{Ldi}{dt}$
$L\to$ volt.second/ampere
$E=\cfrac{1}{2}Li^2$
$L\to $joule/(ampere$)^2$
$\omega L=X _L$
$L\to$ohm.second
Hence all are correct.

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

A lossless coaxial cable has a capacitance of $7\times { 10 }^{ -11 }$ F and an inductance of $0.39\mu H$. Calculate characteristic impedance of the cable.

  1. 65

  2. 75

  3. 66

  4. 77
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here,$C=7\times { 10 }^{ -11 }F$,
        $L=0.39\times { 10 }^{ -6 }H$

         ${ Z } _{ o }$ As the cable is lossless,
        $\therefore { Z } _{ o }\sqrt { \dfrac { L }{ C }  } =\sqrt { \dfrac { 0.39\times { 10 }^{ -6 } }{ 7\times { 10 }^{ -11 } }  } =75ohm$

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

A source of 220 V is applied in an A C circuit . The value of resistance is 220 $\Omega$. Frequency & inductance are 50Hz & 0.7 H then wattless current is 

  1. 0.5 amp

  2. 0.7 amp

  3. 1.0 amp

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A source= $220V$

The value of resistance= $220 \Omega$
Frequency= $50 Hz$
Inductance= $0.7H$
Find the wattless current= ?
Wattless component of current is $i=i _v\sin \theta$
                                                            $=\cfrac {Ev}{z}\sin \theta$
where, $z=$ impedance of $L-R$ circuit
                $=\sqrt {R^2+L^2W^2}$ so,
$i=\cfrac {220}{\sqrt {R^2+L^2+W^2}}\sin \theta$ from impedance triangle,
$\sin \theta= \cfrac {LW}{\sqrt {R^2+L^2W^2}}$
$\Rightarrow i=\cfrac {220}{\sqrt {R^2+L^2W^2}}\cfrac {LW}{\sqrt {R^2+L^2W^2}}$
        $=\cfrac {220}{R^2+L^2W^2}LW$
        $=\cfrac {220 \times 0.7 \times 2 \Pi \times 50}{(220)^2+(0.7\times 2\Pi \times 50)^2}$
        $=\cfrac {220 \times 220}{(220)^2+(220)^2}$
        $=0.5 A$ .

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

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;-

  1. $250 H$
  2. $50H$
  3. $150 H$
  4. $25 H$
Reveal answer Fill a bubble to check yourself
A Correct answer
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),
$L=10R=10\times 25$
$L=250H$

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

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

  1. 6.25 H

  2. 12.5 H

  3. 25 H

  4. 50 H
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

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-

  1. 0.02 H

  2. 0.05 H

  3. 0.01 H

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

$L1=0.01$

$L2=0.03$
$L eff =0.06$

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

Multiple choice introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

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:

  1. 15 kV

  2. 60 kV

  3. 10 kV

  4. 30 kV
Reveal answer Fill a bubble to check yourself
D Correct answer
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.