Power in an AC Circuit

Q. The average power dissipated in a pure inductor of inductance L when an ac current is passing through it, is

1. $\frac{1}{2}L{I}^2$
2. $\frac{1}{4}L{I}^2$
3. $2L{I}^2$
4. $Zero$

Q.

A series RLC circuit contains resistance of 10Ω, an inductance of 0.2H and a capacitor of 100uF .. Its powered by a supply of 200V, 50Hz. Calculate the total circuit impedance, the circuits current, power factor and draw the voltage phasor diagram.

1. z = 10+10j; i = 8.7sin(72.6t - 50); P.F. = 0.35

2. z = 10+31j; i = 8.7sin(50t - 72.6); P.F. = 0.3

3. z = 31j; i = 7.8sin(50t - 72.6); P.F. = 0.4

4. z = 31+30j; i = 8.7sin(72.6t - 50); P.F. = 0.25

Q. An AC source rated $100\text{V (rms)}$ supplies a current of $10\text{A (rms)}$ to a circuit. The average power delivered by the source

1. Must be $1000\text{W}$
2. May be $1000\text{W}$
3. May be greater than 1000 W
4. May be less than 1000 W

Q. A direct current of 2A and alternating current having a maximum value of 2A flow through two identical resistance. The ratio of heat produced in the two resistance will be:

1. 1 : 1
2. 1 : 2
3. 2 : 1
4. 4 : 1

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

1. $\frac{E_0^2}{R}$
2. $\frac{E_0^2}{2R}$
3. $\frac{E_0^2}{4R}$
4. $\frac{E_0^2}{8R}$

Q. What is the r.m.s. value of An alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes in the same resistor

1. 6 amp
2. 2 amp
3. 3.46 amp
4. 0.66 am

Q. An ac supply gives 30 V r.m.s. which passes through a $10\Omega$ resistance. The power dissipated in it is

1. $90\sqrt{2}W$
2. $90W$
3. $45\sqrt{2}W$
   
4. $45W$

Q. What is the r.m.s. value of An alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes in the same resistor

1. 6 amp
2. 2 amp
3. 3.46 amp
4. 0.66 am

Q. The self inductance of a choke coil is 10 mH. When it is connected with a 10V dc source, then the loss of power is 20 watt. When it is connected with 10 volt ac source loss of power is 10 watt. The frequency of ac source will be

1. 50 Hz
2. 60 Hz
3. 80 Hz
4. 100 Hz

Q. An alternating e.m.f. of angular frequency $\omega$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

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

Q.

Power delivered by the source of the circuit becomes maximum, when .

1. $\omega L$=$\omega C$
2. $\omega L$=-$\frac{1}{{\left(\omega C\right)}^2}$
3. $\omega L$=$\sqrt{\omega C}$
4. $\omega L$=$\frac{1}{\omega C}$