Tag: electromagnetic induction and alternating currents

Questions Related to electromagnetic induction and alternating currents

If the number of turns and length of the long solenoid are doubled without changing the area, then its self-inductance $L$ will be:

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. same

  2. 2 times

  3. 3 times

  4. 4 times

Show answer
Correct Option: B
Explanation:
$N$=total number of turns in solenoid
$l$=length of solenoid
$R$=radius of cross section of solenoid
Magnetic field inside solenoid =$B=\mu _o \dfrac{N}{l}i$  where, $\dfrac{N}{l}$=number of turns per unit length

Now, emf induced= $E=NBA$

$\implies E=N\times \mu _o\dfrac{N}{l}i\times \pi R^2$

$\implies E=\dfrac{\mu _{o}N^2\pi R^2}{l}i=Li$
                                                                                    where $L$=self inductance
                                      
Thus, $L=\dfrac{\mu _o N^2 \pi R^2}{l}$

$\implies L\propto \dfrac{N^2}{l}$

Hence, on doubling both $N$ and $l$,

$L$ becomes twice.

Answer-(B)

Self inductance of a long solenoid is directly proportional to-
(Where $L$ is the length of solenoid)

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $L$

  2. $L^2$

  3. $1/L$

  4. $1/L^2$

Show answer
Correct Option: C
Explanation:
$N$=total number of turns in solenoid
$l$=length of solenoid
$R$=radius of cross section of solenoid
Magnetic field inside solenoid =$B=\mu _o \dfrac{N}{l}i$  where, $\dfrac{N}{l}$=number of turns per unit length

Now, emf induced= $E=NBA$

$\implies E=N\times \mu _o\dfrac{N}{l}i\times \pi R^2$

$\implies E=\dfrac{\mu _{o}N^2\pi R^2}{l}i=Li$
                                                                                    where $L$=self inductance
                                      
Thus, $L=\dfrac{\mu _o N^2 \pi R^2}{l}$

Hence, $L\propto \dfrac{1}{l}$

Answer-(C)

Self inductance of a long solenoid is directly proportional to 
($N$ is no. of turns in solenoid)

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $N$

  2. $N^2$

  3. $1/N$

  4. $1/N^2$

Show answer
Correct Option: B
Explanation:
$N$=total number of turns in solenoid
$l$=length of solenoid
$R$=radius of cross section of solenoid
Magnetic field inside solenoid =$B=\mu _o \dfrac{N}{l}i$  where, $\dfrac{N}{l}$=number of turns per unit length

Now, emf induced= $E=NBA$

$\implies E=N\times \mu _o\dfrac{N}{l}i\times \pi R^2$

$\implies E=\dfrac{\mu _{o}N^2\pi R^2}{l}i=Li$
                                                                                    where $L$=self inductance
                                      
Thus, $L=\dfrac{\mu _o N^2 \pi R^2}{l}$

Hence, $L\propto N^2$

Answer-(B)

If area of a long solenoid is doubled,length is trippled and no. of turns are remained contant.Then its self-inductance will be changed how many times-

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $1/3$

  2. $2/3$

  3. $1/9$

  4. $4/3$

Show answer
Correct Option: B
Explanation:
$N$=total number of turns in solenoid
$l$=length of solenoid
$R$=radius of cross section of solenoid
Magnetic field inside solenoid =$B=\mu _o \dfrac{N}{l}i$  where, $\dfrac{N}{l}$=number of turns per unit length

Now, emf induced= $E=NBA$

$\implies E=N\times \mu _o\dfrac{N}{l}i\times A$

$\implies E=\dfrac{\mu _{o}N^2A}{l}i=Li$
                                                                                    where $L$=self inductance
                                      
Thus, $L=\dfrac{\mu _o N^2 A}{l}$

Hence, on doubling area and tripling the length of solenoid,

$L$ becomes $\dfrac{2}{3}$ times.


Answer-(B)

When the speed at which a conductor is moved through a magnetic field is increased, the induced voltage

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. increases

  2. decreases

  3. remains constant

  4. reaches zero

Show answer
Correct Option: A
Explanation:

$E=vBl$    where $v$=speed of conductor


Hence, on increasing speed of conductor , induced voltage increases..

Answer-(A)

Reactance of a coil is $157\Omega$. On connecting the coil across a source of frequency $ 100Hz$, the current lags behind e.m.f. by ${ 45 }^{ o }$. The inductance of the coil is _________.

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $0.25 H$

  2. $0.5 H$

  3. $4H$

  4. $314 H$

Show answer
Correct Option: A
Explanation:

Since the phase angle is $45^{\circ}$,

$\dfrac{X _L}{R}=tan\phi=tan45^{circ}=1$
$\implies X _L=R$
$\implies \omega L=R$
$\implies 2\pi f L=R$
$\implies L=\dfrac{R}{2\pi f}$
$=\dfrac{157}{2\pi\times 100}H$
$=0.25H$

The electrical analog of mass is

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. Diode

  2. Capacitance

  3. Inductance

  4. Resistance

Show answer
Correct Option: C
Explanation:

As per mechanical-electrical analog, displacement is analogous to charge and force analogous to voltage.

From newton's second law of motion,
$F = m \cfrac{d^2x}{dt^2}$

For a diode, voltage and current are exponentially related and is non-linear.
For capacitance,  $V = \cfrac{Q}{C}$
For inductance, $V = L\cfrac{dI}{dt} = L\cfrac{d^2 q}{dt^2}$
For resistance, $V = IR = R \cfrac{dq}{dt}$

By comparing the above equations, it can be concluded that electrical analog of mass is inductance. 

Which of following circuit element stores energy in electromagnetic field?

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. inductor

  2. condenser

  3. variable resistor

  4. capacitor

Show answer
Correct Option: A
Explanation:

Inductor stores energy in the electromagnetic field.
Capacitor and condenser stores energy in the electrostatic field and resistance doesn't store energy in any field.

Find the necessary inductance. if 110 V, 10 W rating bulb is to be used with 220 V A.C source having frequency 50 Hz.

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. L=8.90 H

  2. L=6.75 H

  3. L=7.25 H

  4. L=6.5 H

Show answer
Correct Option: B
Explanation:

Given, $V=110v$ ,$P=10W$ ,$V _0=220 w$ ,$f=50Hz$

Current through series inductor,
Current through bulb=$\dfrac{P}{V}=\dfrac{10W}{110V}=0.09A$
Voltage across inductor,$V _{ind}=\sqrt{V _0^{2} -V^{2}}$=$\sqrt{220^{2}-110^2}=191V$
Reactance of inductor,$R=\dfrac{V _{ind}}{I}=\dfrac{191}{0.09}=2122.22$
Also,$R=2 \pi fL$ or $L$=$\dfrac{R}{2 \pi f}$=$\dfrac{2122.22}{2 \pi 50}$=$6.75H$

The coefficient of mutual inductance between two coils depends on

mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

  1. medium between the coils

  2. separation between the two coils

  3. orientation of the two coils

  4. all of the above

Show answer
Correct Option: D
Explanation:

The flux linked with two coils will depend upon the angle between the two coils. If their planes are parallel, then magnetic flux from one would completely  pass through the other. If the planes are perpendicular, no flux due to any of the coils would flow through the other.

The size of the two coils may be different which will affect the number of lines crossing the coil. The medium, if magnetic, will concentrate the field lines. Thus, all parameters would affect the inductance between them.