Power Factor

Q. The power factor of LCR circuit at resonance is

1. 0.707
2. 1
3. Zero
4. 0.5

Q. Power factor is the ratio of resistance and total impedance (R/Z)

1. True
2. False

Q. In pure Inductor, power factor will always be zero.

1. False
2. True

Q. In an ac circuit, the current is given by $i=5sin(100t-\frac{\pi }{2})$ and the ac potential is $V=200sin\left(100\right)volt.$ Then the power consumption is

1. 20 watts
2. 40 watts
3. 1000 watts
4. 0 watt

Q. The potential differences across the resistance, capacitance and inductance are $80V,40V$ and $100V$ respectively in an L-C-R circuit. The power factor of this circuit is

1. $0.8$
2. $1.0$
3. $0.4$
4. $0.5$

Q. In pure Inductor, power factor will always be zero.

1. False
2. True

Q. Average power in an A.C circuit is 50 watt. Resistance of circuit is $32\Omega$, and source voltage is 50V. Power factor of this circuit is

1. $0.8$
2. $0.6$
3. $\frac{3}{5}$
4. $\frac{3}{4}$

Q. If power factor is $\frac{1}{2}$ in a series RL circuit R = 100$\Omega$. AC mains is used then L is

1. $\frac{\sqrt{3}}{\pi }$ Henry
2. $\pi$ Henry
3. $\frac{\pi }{\sqrt{3}}$ Henry
4. None of these

Q. The Real power consumed is

1. Product of RMS voltage, RMS current and power factor
2. Product of RMS voltage and RMS current
3. Product of average voltage, average current and power factor
4. Product of average voltage and average current

Q. The series combination of resistance $R$ and inductance $L$ is connected to an alternating source of e.m.f. $E=311\sin \left(100\pi t\right)$. If the peak value of wattless current is $0.5\text{A}$ and the impedance of the circuit is $311\Omega$, the power factor will be

1. $\frac{1}{2}$
2. $\frac{\sqrt{3}}{2}$
3. $\frac{1}{\sqrt{3}}$
4. $\frac{1}{\sqrt{5}}$

Q. Power factor is the ratio of real power to apparent power.

1. False
2. True

Q. $\frac{25}{\pi }\mu F$ capacitor and 3000-ohm resistance are joined in series to an ac source of 200 volt and $50se{c}^{-1}$ frequency.The power factor of the circuit and the power dissipated in it will respectively

1. 0.6, 0.06 W
2. 0.06, 0.6 W
3. 0.6, 4.8 W
4. 4.8, 0.6 W

Q. A lamp consumes only $50\%$ of peak power in an a.c. circuit. What is the phase difference between the applied voltage and the circuit current

1. $\frac{\pi }{6}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{4}$
4. $\frac{\pi }{2}$

Q.

An rms voltage of 110 V is applied across a RLC series circuit having a resistance 11W and an impedance 22W. The power consumed is

1. 275 W

2. 366 W

3. 550 W

4. 1100 W

Q. The Real power consumed is

1. Product of RMS voltage, RMS current and power factor
2. Product of RMS voltage and RMS current
3. Product of average voltage, average current and power factor
4. Product of average voltage and average current

Q. A box and a capacitor C are in series across an AC source of $w=2rad{s}^{-1}$. The power factor of the box is $\frac{1}{\sqrt{2}}$ and that of the circuit is 1. Find the impedance of the box.

1. $\frac{1}{C}$
2. $\frac{2}{C}$
3. $\frac{\sqrt{2}}{C}$
4. $\frac{1}{\sqrt{2}C}$

Q. Power factor is cosine of phase difference between supply voltage and current.

1. False
2. True

Q. In an ac circuit, the current is given by $i=5sin(100t-\frac{\pi }{2})$ and the ac potential is $V=200sin\left(100\right)volt.$ Then the power consumption is

1. 20 watts
2. 40 watts
3. 1000 watts
4. 0 watt

Q. An electric dipole is formed by two equal and opposite charges $q$ with separation $d$. The charges have same mass $m$. It is kept in a uniform electric field $E$. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$ is:
$\left[\text{Mains-2019, April 8th, Shift 2}\right]$

1. $\sqrt{\frac{2qE}{md}}$
2. $2\sqrt{\frac{qE}{md}}$
3. $\sqrt{\frac{qE}{2md}}$
4. $\sqrt{\frac{qE}{md}}$

Q. If power factor is $\frac{1}{2}$ in a series RL circuit R = 100$\Omega$. AC mains is used then L is

1. $\frac{\sqrt{3}}{\pi }$ Henry
2. $\pi$ Henry
3. $\frac{\pi }{\sqrt{3}}$ Henry
4. None of these

Q. The r.m.s. current in an ac circuit is 2 A. If the watt less current be $\sqrt{3}$ A , what is the power factor

1. $\frac{1}{\sqrt{3}}$
2. $\frac{1}{3}$
3. $\frac{1}{\sqrt{2}}$
4. $\frac{1}{2}$

Q. A lamp consumes only $50\%$ of peak power in an a.c. circuit. What is the phase difference between the applied voltage and the circuit current

1. $\frac{\pi }{6}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{4}$
4. $\frac{\pi }{2}$

Q. Consider the following diagram. In which of the two circuits does current lead the voltage?

1. (a)
2. (b)
3. Neither (a) nor (b)
4. Both (a) and (b)

Q. A lamp consumes only $50\%$ of peak power in an a.c. circuit. What is the phase difference between the applied voltage and the circuit current

1. $\frac{\pi }{6}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{4}$
4. $\frac{\pi }{2}$

Q. If a current I given by $I_{0}sin(\omega t-\frac{\pi }{2})$ flows in an ac circuit across which an ac potential of $E=E_{0}sin\omega t$ has been applied, then the power consumption P in the circuit will be

1. $P=\frac{E_0{I}_0}{\sqrt{2}}$
2. $P=\sqrt{2}{E}_0{I}_0$
3. $P=\frac{E_0{I}_0}{2}$
4. $P=0$