Tag: electromagnetic induction and alternating currents

Questions Related to electromagnetic induction and alternating currents

A coil of self inductance $2H$ carries a $2A$ current. If direction of current is reversed in $1\ sec$., then induced emf in it:

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $-8V$

  2. $8V$

  3. $-4V$

  4. $Zero$

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Correct Option: B
Explanation:

We know that 

                           $E = \dfrac{ldi}{dt} = 0$

Since current of 2 amperer reverses in 2 second
E.M.F. developed is 
                                 $E = L \times \dfrac{2- (-2)}{1}$
                                  $ E = 2H \times 4As^{-1}$
                                  $E = 8v$
Hence (B) is correct answer

A coil has self-inductance $L = 0.04\, H$ and resistance $R = 12 \Omega$ , connected to $220 V$, 50 Hz supply, what will be the current flow in the coil ?

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. 11.7 A

  2. 12.7 A

  3. 10.7 A

  4. 14.7 A

Show answer
Correct Option: B
Explanation:

Given, $L = 0.04 \, H, R= 12\Omega$
$V= 220$ volt and $f= 50 Hz$
The value of current
$I=\dfrac {V}{Z}$
or or $ I=\dfrac {V}{\sqrt{R^2+(\omega L)^2}}$
or $I=\dfrac {V}{\sqrt{R^2+(2\pi fL)^2}}$
or $I=\dfrac {220}{\sqrt{144+(2\pi50\times 0.04)^2}}$
$\Rightarrow I= 12.7\, A$

What is the rms value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of $2$ amperes in the same resistor:

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $6$ amp

  2. $2$ amp

  3. $3.46$ amp

  4. $0.66$ amp

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Correct Option: A

When $100$ volt D.C is applied across a coil, a current of one ampere flows through it, when $100V$ ac of $50Hz$ is applied to the same coil, only $0.5amp$ flows. Calculate the resistance and inductance of the coil.

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $300\Omega ,\left( \sqrt { 3 } /\pi  \right) Hz$

  2. $100\Omega ,\left( \sqrt { 3 } /\pi  \right) Hz$

  3. $200\Omega ,\left( \sqrt { 3 } /\pi  \right) Hz$

  4. $400\Omega ,\left( \sqrt { 3 } /\pi  \right) Hz$

Show answer
Correct Option: B

An alternating current of $1.5mA$ and angular frequency $\omega=300rad/s$ flows through $10k\Omega$ resistor and a $0.50\mu F$ capacitor in series. Find the RMS voltage across the capacitor and impedance of the circuit?

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $20V,12\Omega$

  2. $10V,12\Omega$

  3. $10V,13\Omega$

  4. $40V,12\Omega$

Show answer
Correct Option: B

A sinusoidal voltage ${ V } _{ 0 }\sin { \omega t } $ is applied across a series combination of resistance R and inductor L. The amplitude of the current in the circuit is :

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $\cfrac { { V } _{ 0 } }{ \sqrt { { R }^{ 2 }+{ \omega }^{ 2 }{ L }^{ 2 } } } $

  2. $\cfrac { { V } _{ 0 } }{ \sqrt { { R }^{ 2 }-{ \omega }^{ 2 }{ L }^{ 2 } } } $

  3. $\cfrac { { V } _{ 0 } }{ \sqrt { { R }^{ 2 }+{ \omega }^{ 2 }{ L }^{ 2 } } } \sin { \omega t } \quad $

  4. ${ V } _{ 0 }/R$

Show answer
Correct Option: B
Explanation:

Impedance of the circuit $\sqrt { { R }^{ 2 }+{ \omega  }^{ 2 }{ L }^{ 2 } } $
Amplitude of voltage$={V} _{0}$
$\therefore$ Amplitude of current $\cfrac { { V } _{ 0 } }{ \sqrt { { R }^{ 2 }-{ \omega  }^{ 2 }{ L }^{ 2 } }  } $

An ideal choke takes a current of $8A$ when connected to an a.c source of $100volt$ and $50Hz$. A pure resistor under the same conditions takes a current of $10A$. If two are connected in series to an a.c supply of $100V$ and $40Hz$, then the current in the series combination of above resistor and inductor is :

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $10A$

  2. $8A$

  3. $5\sqrt{2}$ amp

  4. $10\sqrt {2}$ amp

Show answer
Correct Option: C
Explanation:

${ X } _{ L }=\cfrac { 100 }{ 8 } ;R=\cfrac { 100 }{ 10 } =10\Omega $
$L\times 100\pi =\cfrac { 100 }{ 8 } $
$L=\cfrac { 1 }{ 8\pi  } H$
$Z=\sqrt { { \left( \cfrac { 1 }{ 8\pi  } \times 2\pi \times 40 \right)  }^{ 2 }+{ 10 }^{ 2 } } =10\sqrt { 2 } $
$I=\cfrac { E }{ Z } =\cfrac { 100 }{ 10\sqrt { 2 }  } =\cfrac { 10 }{ \sqrt { 2 }  } =5\sqrt { 2 } A$

A coil of negligible resistance is connected in series with $90\Omega$ resistor across a $120V-60Hz$ line. A voltmenter reads $36V$ across the resistance. Find the voltage across the coil and inductance of the coil.

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $114V,1.76H$

  2. $114.5V,0.76H$

  3. $114V,0.86H$

  4. $144V,0.76H$

Show answer
Correct Option: B
Explanation:

$V=\sqrt{V _R^2+V _L^2}\ \therefore V _L=\sqrt{V^2-V _R^2}\=114.5V\V _R=IR\ \Rightarrow I+\cfrac{36}{90}=0.4A\ \therefore V _L=IX _L\=I\omega L\ \therefore L=\cfrac{V _L}{I\omega}=\cfrac{114.5}{0.4\times2\pi\times60}\=0.76H$

A $200km$ long telegraph wire has capacity of $0.014\mu F/km$. If it carries an alternating current of $50KHz$, what should be the value of an inductance required to be connected in series so that impedance is minimum?

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $0.703H$

  2. $0.303H$

  3. $0.503H$

  4. $0.603H$

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Correct Option: A

A $0.19H$ inductor and a $80\Omega$ resistance connected in series to a $220V, 50Hz$ ac source. Calculate the current in the circuit and the phase angle between the current and the source voltage.

ac voltage applied to a series lr circuit lr circuit phase relations between alternating voltage and alternating current in different types of alternating current circuits and phasor diagram electromagnetic induction and alternating currents physics

  1. $2.2A, tan^{-1} ({3 \over 4})$

  2. $3A, tan^{-1} ({2 \over 5})$

  3. $5A, tan^{-1} ({8 \over 9})$ 

  4. $6A, tan^{-1} ({7 \over 5})$

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Correct Option: A