Power Factor

Q. Resonant frequency of a series LCR circuit is 600Hz.Quality factor of the circuit is 4.Band with is?

Q. A carnot engine has efficiency of 80%. If its sink is at 127°C, then find the temperature of source.

Q. If carnot engine works between 127 degree Celsius to 527 degree Celsius then its efficiency is A) 25% B)37.5% C)50% D)75%

Q. The work done per unit volume to stretch the length of area of cross section 2mm2 by 2% will be (Y=810 to the power 10N/m2) 1)40MJ/m3 2)16 " 3)64 " 4)32 "

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. Calculate the time for which a motor pump of 10HP and effiency 80% must be switched on so, as to pump 50 kg of water through a vertical height of 20m.[g=10m/s2;1HP=758W].

Q. Which of the following results is true?

1. $PowerFactor=\frac{ApparentPower}{RealPower}$
2. $PowerFactor=\frac{RealPower}{ApparentPower}$
3. $PowerFactor=\frac{ReactivePower}{RealPower}$
4. $PowerFactor=\frac{ReactivePower}{ApparentPower}$

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. In an ac circuit, the instantaneous values of e.m.f. and current are e = 200 sin 314 t volt and $i=sin(314t+\frac{\pi }{3})$ ampere. The average power consumed in watt is

1. 200
2. 100
3. 50
4. 25

Q. In $\text{XY}-$plane, there is surface charge density of $5\times {10}^{-16}{\text{Cm}}^{-2}$ on a long uniformly charged sheet. A circular loop of radius $0.1\text{m}$ makes an angle of ${60}^{\circ }$ with $\text{Z-}$axis. Determine the electric flux through the loop ?

1. $7.68\times {10}^{-9}{\text{Nm}}^2{\text{C}}^{-1}$
2. $7.68\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$
3. $9.46\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$
4. $9.46\times {10}^{-9}{\text{Nm}}^2{\text{C}}^{-1}$

Q. Power factor of an $L-R$ series circuit is $0.6$ and that of a $C–R$ series circuit is $0.5$. If the elements $(L,C,$ and $R)$ of the two circuits are joined in series, the power factor of this circuit is found to be $1$. The ratio of the resistance in the $L-R$ circuit to the resistance in the $C-R$ circuit is

1. $\frac{6}{5}$
2. $\frac{4}{3\sqrt{3}}$
3. $\frac{5}{6}$
4. $\frac{3\sqrt{3}}{4}$

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 power factor of the circuit in below figure is $\frac{1}{\sqrt{2}}$. The capacitance of the circuit is equal to

1. $400\mu F$
2. $300\mu F$
3. $500\mu F$
4. $200\mu F$

Q. In an ac circuit with voltage V and current I, the power dissipated is

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

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. In $\text{XY}-$plane, there is surface charge density of $5\times {10}^{-16}{\text{Cm}}^{-2}$ on a long uniformly charged sheet. A circular loop of radius $0.1\text{m}$ makes an angle of ${60}^{\circ }$ with $\text{Z-}$axis. Determine the electric flux through the loop ?

1. $7.68\times {10}^{-9}{\text{Nm}}^2{\text{C}}^{-1}$
2. $7.68\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$
3. $9.46\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$
4. $9.46\times {10}^{-9}{\text{Nm}}^2{\text{C}}^{-1}$

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. A 16 ohms loudspeaker and an 8 ohms loudspeaker are connected in parallel across a terminals of an amplifier. Assuming the speakers behave as resistors, calculate the total resistance of the two speakers

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. what are the direction of current in the galvanometer of unbalanced wheatstone bridge? and how to identify them

Q. The instantaneous values of alternating current and voltages in a circuit are given as,
$i=\frac{1}{\sqrt{2}}\sin \left(100\pi t\right)\text{A}$ and
$E=\frac{1}{\sqrt{2}}\sin (100\pi t+\frac{\pi }{3})\text{V}$
The average power (in watts) consumed in the circuit is,

1. $\frac{1}{8}$
2. $\frac{\sqrt{3}}{4}$
3. $\frac{1}{4}$
4. $\frac{1}{2}$

Q. An alternating e.m.f. is applied to purely capacitive circuit. The phase relation between e.m.f. and current flowing in the circuit is or
In a circuit containing capacitance only

1. e.m.f. is ahead of current by $\frac{\pi }{2}$
2. Current is ahead of e.m.f. by $\frac{\pi }{2}$
3. Current lags behind e.m.f. by $\pi$
4. Current is ahead of e.m.f. by $\pi$

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