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Multiple choice 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

A.c across L-R,L-C and L-C-R series circuits. In an LR circuit, $R=10\Omega$ and $L=2H$, If an alternating voltage of $120V$ and $60Hz$ is connected in this circuit, then the value of current flowing in it will be _____ A (nearly)

  1. $0.32$

  2. $0.16$

  3. $0.48$

  4. $0.8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Impedance Z = sqrt(R^2 + (2*pi*f*L)^2). R = 10, L = 2, f = 60. XL = 2 * 3.14 * 60 * 2 = 753.6. Z = sqrt(100 + 567913) approx 754. Current I = V/Z = 120 / 754 approx 0.16 A.

Multiple choice 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

An L-C-R series circuit with $100\omega$ resistance is connected to an A.C source of 200 V and angular frequency $300 rad\,s^{-1}$. When only the capacitor is removed, the current lags behind the voltage by $60^0$ . When only inductor is removed, the current leads the voltage by $60^0$. If all elements are connected , the current in the circuit is

  1. 0.5 A

  2. 1.5 A

  3. 2 A

  4. 2.5 A
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given R = 100. When C is removed (LR circuit), tan(60) = XL/R => XL = 100 * sqrt(3) = 173.2. When L is removed (RC circuit), tan(60) = XC/R => XC = 100 * sqrt(3) = 173.2. Since XL = XC, the circuit is at resonance when all elements are connected. At resonance, Z = R = 100. Current I = V/R = 200 / 100 = 2 A.

Multiple choice 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

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

  1. $-8V$

  2. $8V$

  3. $-4V$

  4. $Zero$
Reveal answer Fill a bubble to check yourself
B Correct answer
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

Multiple choice 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

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 ?

  1. 11.7 A

  2. 12.7 A

  3. 10.7 A

  4. 14.7 A
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $I=\dfrac {220}{\sqrt{144+(2\pi50\times 0.04)^2}}$
$\Rightarrow I= 12.7\, A$

Multiple choice 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

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:

  1. $6$ amp

  2. $2$ amp

  3. $3.46$ amp

  4. $0.66$ amp
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice 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

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.

  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. $400\Omega ,\left( \sqrt { 3 } /\pi  \right) Hz$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For DC, R = V/I = 100/1 = 100 ohms. For AC, Z = V/I = 100/0.5 = 200 ohms. Since Z^2 = R^2 + (wL)^2, then 200^2 = 100^2 + (2*pi*50*L)^2. Solving for L gives sqrt(30000)/(100*pi) = sqrt(3)/pi H. The unit Hz in the option is a typo for H.

Multiple choice 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

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?

  1. $20V,12\Omega$

  2. $10V,12\Omega$

  3. $10V,13\Omega$

  4. $40V,12\Omega$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Voltage across capacitor V_c = I_rms * X_c = I_rms * (1/(w*C)). Given I_rms = 1.5mA, w = 300, C = 0.5uF, V_c = 0.0015 / (300 * 0.5 * 10^-6) = 0.0015 / 0.00015 = 10V. Impedance Z = sqrt(R^2 + X_c^2). With R = 10k ohms and X_c = 1/(300 * 0.5 * 10^-6) = 6666 ohms, Z is approx 12k ohms. Option B is the closest match.

Multiple choice 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

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 :

  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. ${ V } _{ 0 }/R$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 } }  } $

Multiple choice 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

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 :

  1. $10A$

  2. $8A$

  3. $5\sqrt{2}$ amp

  4. $10\sqrt {2}$ amp
Reveal answer Fill a bubble to check yourself
C Correct answer
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 } $
$I=\cfrac { E }{ Z } =\cfrac { 100 }{ 10\sqrt { 2 }  } =\cfrac { 10 }{ \sqrt { 2 }  } =5\sqrt { 2 } A$

Multiple choice 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

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.

  1. $114V,1.76H$

  2. $114.5V,0.76H$

  3. $114V,0.86H$

  4. $144V,0.76H$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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