Tag: average power in ac circuit and power factor

Questions Related to average power in ac circuit and power factor

In a series LCR circuit,the inductive reactance is twice the resistance and the capacitance reactance is ${\frac{1}{3}^{rd}}$ the inductive reactance. The power factor of the circuit is:

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $0.5$

  2. $0.6$

  3. $0.8$

  4. $1$

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Correct Option: B
Explanation:

$\begin{array}{l}\omega L = 2R\\frac{1}{{\omega C}} = \frac{1}{3}\left( {\omega L} \right)\\omega L - \frac{1}{{\omega C}} = 2R - \frac{{2R}}{3} = \frac{{4R}}{3}\\tan \phi  = \frac{{4R}}{3} \times \frac{1}{R} = \frac{4}{3}\\cos \phi  = \frac{1}{{\sqrt {1 + {{\tan }^2}\phi } }} = \frac{1}{{\sqrt {1 + \frac{{{4^2}}}{{{3^2}}}} }} = \frac{3}{5} = 0.6\end{array}$

In series L.C.R circuit resonance occurs at frequency $f=f _0$, If at this moment amplitude of current is $I _0$ then calculate wattles current at the same moment:-

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $\sqrt 2 \ I _0$

  2. $\dfrac{I _0}{\sqrt2}$

  3. $\dfrac{I _0}{2\sqrt2}$

  4. $Zero$

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Correct Option: B

Which of the following device in alternating circuit provides maximum power

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. Only capacitor

  2. Capacitor and resistor

  3. Only inductor

  4. Only resistor

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Correct Option: A

An alternative current, L.R circuit comprises of an inductor, whose reactance $X _L = 3R$, where $R$ is the resistance of the circuit. If a capacitor, whose reactance $X _C = R$ is connected in series then what will be the ratio of the new and the old power factor?

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $\sqrt{2}$

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

  3. $2$

  4. $1$

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Correct Option: B

In an $LR$-circuit, the inductive reactance is equal to the resistance $R$ of the circuit. an e.m.f. $E=E _{0}\ cos(\omega t)$ applied to the circuit. The power consumed in the circuit is

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $\dfrac{E^{2} _{0}}{R}$

  2. $\dfrac{E^{2} _{0}}{2R}$

  3. $\dfrac{E^{2} _{0}}{4R}$

  4. $\dfrac{E^{2} _{0}}{8R}$

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Correct Option: C

In general in an alternating current circuit for a complete cycle

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. The average value of current is zero

  2. The average value of square of the current is zero

  3. Average power dissipation is zero

  4. All of these

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Correct Option: A

In an a.c. circuit consisting of resistance $R$ and inductance $L$, the voltage across $R$ is $60$ volt and that across $L $ is $80$ Volt.The total Voltage across the combination is 

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $140 V$

  2. $20 V$

  3. $100 V$

  4. $70 V$

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Correct Option: C

Find the resonant frequency and $Q-factor$ of a series $LCR$ circuit with $L = 3.0\ H, C = 27\mu F$ and $R = 7.4\Omega$.

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $111\ rad/s, 45$

  2. $111\ rad/s, 90$

  3. $55.5\ rad/s, 45$

  4. $55.5\ rad/s, 90$

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Correct Option: A

The self inductance of a choke coil is mH. when it is connected with a 10 VDC source then the loss of power is 20 watt. When it connected with 10 volt AC source loss of power is 10 watt. The frequency of AC source will bw-

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. 50 Hz

  2. 60 Hz

  3. 80 Hz

  4. 100 Hz

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} When\, \, \, dc\, \, is\, \, pass\, \, through\, \, the\, \, inductor\, \, no\, \, induv\tan  ce\, \, effect\, \, will\, \, be\, \, their\, \, only \ resis\tan  ce\, \, will\, \, be\, their\, \, resis\tan  ce\, \, of\, \, the\, \, inductor\, \, be\, \, R \ 20=\frac { { 100 } }{ R }  \ R=5\Omega  \ Xl=\omega \times 0.001 \ power\, \, =\frac { { { v^{ 2 } } } }{ z } \cos  \phi  \ Z=\sqrt { 25+{ \omega ^{ 2 } }\times { { 10 }^{ -6 } } }  \ \cos  \phi =\frac { R }{ Z } =\frac { 5 }{ Z }  \ 10=\frac { { 100 } }{ Z } \frac { 5 }{ Z } =\frac { { 500 } }{ { { Z^{ 2 } } } } =\frac { { 500 } }{ { 25 } } +{ \omega ^{ 2 } }\times { 10^{ -6 } } \ 25+{ \omega ^{ 2 } }\times { 10^{ -6 } }=50 \ { \omega ^{ 2 } }=25\times { 10^{ 6 } } \ \omega =5000 \end{array}$
$=50 Hz$
Hence, Option $A$ is correct answer.

For watt-less power in an $AC$ circuit the phase angle between the current and voltage is

physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

  1. $0^o$

  2. $90^o$

  3. $45^o$

  4. Not possible

Show answer
Correct Option: B
Explanation:

Watt-less power in an AC circuit is basically power supposed to be generated by inductive and capacitive reactance and since they are not resistor they generate any heat , and these power wasted is called watt-less power and its phase angle is always $90^o$ as it has only capacitor and inductor.