Q. No.A LCR series circuit driven with \(E_{r m s}=90 ~\text{V}\) at frequency \(f_d=30~\text{Hz}\) has resistance \(R=80~\Omega,\) an inductance with inductive reactance \(X_L=20.0~\Omega\) and capacitance with capacitive reactance \(X_C=80.0~\Omega.\) The power factor of the circuit is:
1. \(0.8\)
2. \(0.64\)
3. \(0.9\)
4. \(0.5\)
1. \(0.8\)
2. \(0.64\)
3. \(0.9\)
4. \(0.5\)
Subtopic: Power factor |
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Level 1: 80%+
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An inductor of \(10~\text{mH}\), capacitor of \(0.1 ~\mu \text{F}\) and a resistor of \(100~\Omega\)
1. \(100\)
2. \(300\)
3. \(500\)
4. \(600\)
1. \(100\)
2. \(300\)
3. \(500\)
4. \(600\)
Subtopic: Power factor |
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Level 2: 60%+
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For the series \(\text L\text C\text R\) circuit connected with \(220~\text V \), \(50~\text{Hz}~\text {a.c}\) source as shown in the figure, the power factor is \(\dfrac{a}{10}.\) The value of \(a\) is:
1. \(4\)
2. \(10\)
3. \(6\)
4. \(8\)
1. \(4\)
2. \(10\)
3. \(6\)
4. \(8\)
Subtopic: Power factor |
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A capacitor of reactance \(4 \sqrt{3}~\Omega\) and a resistor of resistance \(4 ~\Omega\) are connected in series with an ac source of peak value \(8 \sqrt{2} \mathrm{~V}\). The power dissipation in the circuit is ________ \(\text W\).
1. \(2\)
2. \(4\)
3. \(8\)
4. \(16\)
1. \(2\)
2. \(4\)
3. \(8\)
4. \(16\)
Subtopic: Power factor |
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Level 2: 60%+
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If a series AC circuit has \(L=\dfrac{1}{10 \pi}~\text{H},\) \(C=\dfrac{1}{1000 \pi}~\text{F},\) \(R=10~\Omega,\) and is powered by a \(220~\text{V}, 50~\text{Hz}\) source, what is the power factor?
| 1. | \(0.75\) | 2. | \(0.5\) |
| 3. | \(1\) | 4. | none of the above |
Subtopic: Power factor |
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Level 2: 60%+
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The alternating voltage and current in a circuit are given by:
\(V=100\sin(\omega t)~\text{volts}\)
\(I=100 \sin \left(\omega t+\dfrac{\pi}{3}\right)\) milliamperes
The average power dissipated in the circuit is:
\(V=100\sin(\omega t)~\text{volts}\)
\(I=100 \sin \left(\omega t+\dfrac{\pi}{3}\right)\) milliamperes
The average power dissipated in the circuit is:
| 1. | \(2.5~\text{W}\) | 2. | \(5~\text{W}\) |
| 3. | \(10~\text{W}\) | 4. | \(20~\text{W}\) |
Subtopic: Power factor |
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Level 2: 60%+
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An AC circuit with source voltage \(\varepsilon=20\sin(1000t)\) is connected to a series \(L\text{-} R\) circuit whose power factor is \(\dfrac{1}{\sqrt2}.\) If \(E=25\sin(2000t),\) then the new power factor is:
1. \(\dfrac{2}{\sqrt5}\)
2. \(\dfrac{1}{\sqrt{5}}\)
3. \( \dfrac{1}{\sqrt3}\)
4. \( \sqrt{\dfrac{3}{5}} \)
1. \(\dfrac{2}{\sqrt5}\)
2. \(\dfrac{1}{\sqrt{5}}\)
3. \( \dfrac{1}{\sqrt3}\)
4. \( \sqrt{\dfrac{3}{5}} \)
Subtopic: Power factor |
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The average power in an electric circuit if the source voltage \((V)=20 \sin (100 \omega t)\) and current in the circuit \((I)=2 \sin \left(100 \omega t+\frac{\pi}{3}\right) ~\) is:
1. \(10~\text W\)
2. \(20~\text W\)
3. \(5~\text W\)
4. \(15.5~\text W\)
1. \(10~\text W\)
2. \(20~\text W\)
3. \(5~\text W\)
4. \(15.5~\text W\)
Subtopic: Power factor |
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Level 1: 80%+
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In a series \(LCR\) circuit, the resistance \(R,\) inductance \(L,\) and capacitance \(C\) are \(10~\Omega,\) \(0.1~\text{H},\) and \(2~\text{mF},\) respectively. If the angular frequency of the AC source is \(100~\text{rad/s},\) the power factor of the circuit is:
| 1. | \(\dfrac{1}{\sqrt{5}}\) | 2. | \(\dfrac{2}{\sqrt{5}}\) |
| 3. | \(\dfrac{3}{\sqrt{5}}\) | 4. | \(\dfrac{2}{2\sqrt{5}}\) |
Subtopic: Power factor |
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Level 1: 80%+
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| Statement I: | In LCR circuit, by increasing frequency current increases first then decreases |
| Statement II: | Power factor of LCR circuit is one. |
Choose the correct option
| 1. | Statement I is correct and statement II is incorrect |
| 2. | Statement I is incorrect and statement I is correct |
| 3. | Both Statement I and statement II are correct |
| 4. | Both Statement I and statement II are incorrect |
Subtopic: Power factor |
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Level 2: 60%+
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