Tag: introduction to induction

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Questions Related to introduction to induction

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

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

  1. $4$
  2. $8$
  3. $12$
  4. $16$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

The unit of inductance is equivalent to

  1. $\dfrac {volt\times ampere}{second}$
  2. $\dfrac { ampere}{volt\times second}$
  3. $\dfrac {volt}{Ampere\times second}$
  4. $\dfrac {volt\times second}{ampere}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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 

  1. $2$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{4}$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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

  1. Half

  2. Double

  3. Four times

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

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

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

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

  1. $\dfrac{\text {joule}}{(\text{ampere})^2}$
  2. $\dfrac{\text {tesla} - m^2}{(\text{ampere})^2}$
  3. $\text{ohm-second}$
  4. $\dfrac{1}{\text{Farad-second}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

So, Option $D$ is correct.

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

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.

  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 $L\omega$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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 :



  1. $-\in \;and\;r$
  2. $\in \;and\;-r$
  3. $-r\;and\;\in \;$
  4. $r\;and\;-\in$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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