Tag: electromagnetic induction and alternating currents

Questions Related to electromagnetic induction and alternating currents

A solenoid coil is wound on a frame of rectangular cross section. If all the linear dimension of the frame are increased by a factor of two and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $4$

  2. $8$

  3. $12$

  4. $16$

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Correct Option: B
Explanation:

Self inductance, $L = \dfrac{\mu 0 N^2 A}{l}$ _(1)


where N = total number of turns


$n = \dfrac{N}{l}$, where n = number of turns per unit length

$N = nl$ put it in (1)

$L = \dfrac{\mu _0 (n l )^2 A}{l} = \mu _0 n^2 l A$

In the given question n is same
Area will increase by $4$ times
length will increase by $2$ times

$L' = \mu _0 n^2 (2l) (4A) = 8 \mu _0 n^2 lA$

$L' = 8L$ inductance will increased by $8$ times.

The physical quantity which is measured in the unit of Wb $A^{-1}$ is

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. self inductance

  2. mutual inductance

  3. magnetic flux

  4. both (a) and (b)

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Correct Option: D
Explanation:

both (a) and (b) 

self inductance and mutual inductance has same unit both measure magnetic flux per unit area.

The unit of inductance is equivalent to

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\dfrac {volt\times ampere}{second}$

  2. $\dfrac { ampere}{volt\times second}$

  3. $\dfrac {volt}{Ampere\times second}$

  4. $\dfrac {volt\times second}{ampere}$

Show answer
Correct Option: D
Explanation:

$As \, \varepsilon \, = \,  L \, \dfrac{dI}{dt},$
$L \, = \, \varepsilon \dfrac{dt}{dI} \Rightarrow \, L \, = \, \dfrac{volt \times second}{ampere}$

What is the SI unit of self-inductance ?

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. Henry

  2. Tesla

  3. Weber

  4. Gauss

Show answer
Correct Option: A
Explanation:

 Henry (symbol H) is the SI derived unit of self-inductance. 

Two concentric co-planar circular loops of radii $r _1$ and $r _2$ carry currents of respectively $i _1$ and $i _2$ in opposite directions (one clockwise and the other anticlockwise.) The magnetic induction at the centre of loops is half that due to $i _1$ alone at the centre. If $r _2 = 2r _1$. the value of $i _2 / i _1$ is 

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $2$

  2. $\dfrac{1}{2}$

  3. $\dfrac{1}{4}$

  4. $1$

Show answer
Correct Option: D
Explanation:

$\begin{array}{l} B=\frac { { { \mu _{ o } }{ i _{ 1 } } } }{ { 2{ r _{ 1 } } } } -\frac { { { \mu _{ o } }{ i _{ 2 } } } }{ { 2\left( { 2{ r _{ 1 } } } \right)  } }  \ =\frac { { { \mu _{ o } }{ i _{ 1 } } } }{ { 2{ r _{ 1 } } } } -\frac { { { \mu _{ o } }{ i _{ 2 } } } }{ { 4{ r _{ 2 } } } }  \ { B^{ ' } }=\frac { { { \mu _{ o } }{ i _{ 1 } } } }{ { 2{ r _{ 1 } } } }  \ \Rightarrow B=\frac { { { B^{ ' } } } }{ 2 }  \ \Rightarrow \frac { { { \mu _{ o } }{ i _{ 1 } } } }{ { 2{ r _{ 1 } } } } -\frac { { { \mu _{ o } }{ i _{ 2 } } } }{ { 4{ r _{ 1 } } } } =\frac { { { \mu _{ o } }{ i _{ 1 } } } }{ { 4{ r _{ 1 } } } }  \ \Rightarrow \frac { { { \mu _{ o } }{ i _{ 1 } } } }{ { 4{ r _{ 1 } } } } =\frac { { { \mu _{ o } }{ i _{ 2 } } } }{ { 4{ r _{ 1 } } } }  \ \Rightarrow \frac { { { i _{ 1 } } } }{ { { i _{ 2 } } } } =1 \ Hence, \ option\, \, D\, \, is\, \, correct\, \, answer. \end{array}$

When the number of turns in a solenoid is doubled without any change in the length of the solenoid, its self-inductance becomes :

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. Half

  2. Double

  3. Four times

  4. Eight times

Show answer
Correct Option: C
Explanation:

Self-inductance,
$\begin{array}{l}L \propto {N^2}\\therefore \dfrac{{{L _1}}}{{{L _2}}} = {\left( {\dfrac{{{N _1}}}{{{N _2}}}} \right)^2} = {(2)^2} = 4...........{ since,{N _2} = 2{N _1}} \\left[ {{L _2} = 4{L _1}} \right]\end{array}$

Which of the following does not have the same dimensions as the Henry?

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $\dfrac{\text {joule}}{(\text{ampere})^2}$

  2. $\dfrac{\text {tesla} - m^2}{(\text{ampere})^2}$

  3. $\text{ohm-second}$

  4. $\dfrac{1}{\text{Farad-second}}$

Show answer
Correct Option: D
Explanation:

Option $D$ is does not have the same dimensions as the Henry.

So, Option $D$ is correct.

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

Show answer
Correct Option: C
Explanation:

The henry (symbolized H) is the Standard International ( SI ) unit of inductance and it is used to measure inductance.

Therefore, C is correct option.

Alternating current is flowing in inductance L and resistance R. The frequency of source is $\displaystyle\frac{\omega}{2\pi}$. Which of the following statement is correct.

introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. For low frequency the limiting value of impedance is L

  2. For high frequency the limiting value of impedance is $L\omega$

  3. For high frequency the limiting value of impedance is R

  4. For low frequency the limiting value of impedance is $L\omega$

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} \, \, As\, frequency\, approaches\, zero\, or\, DC,\, the\, inducators\, reac\tan  ce\, would\, decrease\, tozero\, , \ acting\, like\, a\, short\, circuit.\, this\, means\, inductive\, reac\tan  ce\, is\, proportional\, to\, fequency \ \, \, \, \, \, \, \, \, \, \, \, \, \, so\, ,\, for\, low\, frequency\, the\, { { limimiting } }\, \, value\, of\, impedance\, is\, L,\, and\, \, alternating\,  \ current\, is\, flowing\, in\, inductance\, L\, and\, resistance\, R.\, \, The\, frequency\, of\, source\, is\, \frac { \omega  }{ { 2\pi  } } . \ so\, the\, correct\, option\, is\, A. \end{array}$

A student measures the terminal potential difference (V) of a cell (of emf $\varepsilon$ and internal) resistance r) as a function of the current (I) flowing through it. The slope and intercept of the graph between V and I, then respectively equal to :



introduction to induction electromagnetic induction electromagnetic induction and alternating currents physics

  1. $-\in \;and\;r$

  2. $\in \;and\;-r$

  3. $-r\;and\;\in \;$

  4. $r\;and\;-\in$

Show answer
Correct Option: C
Explanation:

$E = V + Ir $
$\Rightarrow V=E-Ir$ 
$Comparing\;with\; y = mx + c$ 
$Slope = - r, intercept = E$