Power Factor

Q.

In a series $LR$ circuit, power of $400W$ is dissipated from a source of $250V,50Hz$. The power factor of the circuit is $0.8$. In order to bring the power factor to unity, a capacitor of value $C$ is added in series to the $L$ and $R$. Taking the value of $C$ as $\left(\frac{n}{3\mathrm{\pi }}\right)\mu F$, then the value of $n$ is __________.

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.

A transformer has an efficiency of $80\%$. It is connected to a power input of $5kW$ at $200V$. If the secondary voltage is $250V$, the primary and secondary currents are respectively

1. $25A$, $20A$

2. $20A$, $16A$

3. $25A$, $16A$

4. $40A$, $25A$

5. $40A$, $16A$

Q.

What are the applications of transformers?

Q.

. The phase difference between the current through the resistance and voltage across the resistance in a series LCR circuit is

Q.

A sinusoidal voltage of peak value $250V$ is applied to a series $LCR$ circuit, in which $R=8\Omega$, $L=24mH$ and$C=60\mu F$. The value of power dissipated at resonant conditions is $xkW$. The value of$x$ to the nearest integer is _________.

Q.

Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0 H, C = 32 μF and R = 10 Ω. What is the Q-value of this circuit?

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.

What is the maximum current that can be drawn from a cell of emf E and internal resistance r connected to an external resistance R?

1. I = E/R

2. I = E/(R+r)

3. I = E/r

4. infinite

Q.

A current of 5A is flowing at 220V in the primary coil of a transformer. If the voltage produced in the secondary coil is 220V and 50% of power is lost, then the current in secondary will be:

1. 0.5A

2. 2.5A

3. 5A

4. 0.25A

Q.

The plot given below is of the average power delivered to an LRC circuit versus frequency. The quality factor of the circuit is:

1. 5

2. 2

3. 2.5

4. 4, 0

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

1. 
2. None of these
3. πHenry
4. 

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.

The change in magnetic field lines in a coil is the cause of induced electric current in it. Name the underlying phenomenon.

Q. If a fan of 60 W, two tube lights of 40 W each are used for 5 hours daily, how much electrical energy willbe consumed? Also find the cost of electricity for 30 days if the cost of 1 unit is Rs. 4 00

Q. The power factor of LCR circuit at resonance is

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

Q. A magnet is suspended from a spring as shown in the diagram. When it oscillates, the magnet moves in and out of the coil. The coil is connected to a galvanometer $G$. Then, as the magnet oscillates -

Consider the loss of energy due to various factors.

1. $G$ shows no deflection.
2. $G$ shows deflection to the left and right, but the amplitude steadily decreases.
3. $G$ shows deflection to the left and right with constant amplitude.
4. $G$ shows deflection on one side only.

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

Q. Two identical conductors $P$ and $Q$ are placed on two frictionless, flat, conducting rails $R$ and $S$, in a uniform magnetic field directed into the plane. If conductor $P$ is moved in the direction shown in the figure with a constant speed, then the conductor $Q$ -

1. will be attracted towards conductor $P$
2. will be repelled away from conductor $P$
3. will remain stationary
4. first attracted and then repelled away from conductor $P$

Q. In a circuit containing an inductance of zero resistance, the e.m.f. of the applied ac voltage leads the current by

1. ${90}^{\circ }$
2. ${30}^{\circ }$
3. $0^{\circ }$
4. ${45}^{\circ }$

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.

The average power dissipation in pure capacitive circuit is:

1. 

2. 

3. zero

4. 

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

Q. ntThe phase difference between current and voltage, when the freqeuency of applied emf is w + R/2L (w is resonance frequency) in a series LCR circuit isn nt(a) pi/2 (b) pi/4 (c)pi/6 (d)0n

Q. Find the energy stored in the circuit containing four capacitors at the steady state.

1. $99\mu \text{J}$
2. $49.5\mu \text{J}$
3. $62\mu \text{J}$
4. $75\mu \text{J}$

Q. 47. In an AC circuit , maximum value of voltage is 423 volts. Its effective voltage?

Q. For an RLC circuit driven with voltage of amplitude $v_m$ and frequency ${\omega }_0=\frac{1}{\sqrt{LC}}$, the current exhibits resonance. The quality factor, Q, is given by

1. $\frac{R}{\left({\omega }_{0}C\right)}$
2. $\frac{CR}{{\omega }_0}$
3. $\frac{{\omega }_{0}L}{R}$
4. $\frac{{\omega }_{0}R}{L}$

Q. A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage $\left(U\right)$ as $ϵ=\alpha U$ where $\alpha =2V^{-1}$. A similar capacitor with no dielectric is charged to $U_0=78V$. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

Q.

Two equal resistance are connected in the gaps of a metre bridge if the resistance in the left is increased by 10% the balancing point shifts

1.10% to right

2.10% to left

3.9.6%to right

4.4.8% to right

Q. In a chamber, a uniform magnetic field of $6.5G(1G={10}^{-4}\text{T})$ is maintained. An electron is shot into the field with a speed of $4.8\times {10}^6\text{~m}/\text{s}$ normal to the field. Obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain
Take $(e=1.6\times {10}^{-19}\text{C},m_{\theta }=9.1\times {10}^{-31}\text{kg})$.