Power in an AC Circuit

Q. An LCR series circuit with a resistance of 100 ohm is connected to an ac source of 100 V (r.m.s.) and angular frequency 300 rad/s. When only the capacitor is removed, the current lags behind the voltage by . When only the inductor is removed the current leads the voltage by . The average power dissipated is

1. 50 W
2. 100 W
3. 200 W
4. 400 W

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. 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. 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.

Why is choke coil preferred over resistor to reduce a.c?

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

Q.

A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

Q. In a series RLC circuit, the r.m.s voltage across the resistor and the inductor are respectively 400V and 700V. If the equation for the applied voltage is e=500\ast2^1/2sinwt, then the peak voltage across the capacitor is(1)1200V(2)1200\ast2^1/2V(3)400V(4)400\ast2^1/2V

Q. A bulb is connected first with dc and then ac of same voltage then it will shine brightly with

1. Brightness will be in ratio $\frac{1}{1.4}$
2. AC
3. Equally with both
4. DC

Q. The average power dissipation in a pure capacitance in ac circuit is

1. $\frac{1}{2}C{V}^2$
2. $C{V}^2$
3. $\frac{1}{4}C{V}^2$
4. $Zero$

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

Q. A choke coil is preferred to a rheostat in ac circuit as

1. It increases voltage
2. It consumes almost zero power
3. It increases current
4. It increases power

Q. a heater coil connected across a given potential difference has power P. now the coil is cut into two equal halves and joined in parellel . across the same potential difference , this combination has power ?

Q. (i) When an AC source is connected to an ideal inductor, show that the average power supplied by the source over a complete cycle is zero.

(ii) A lamp is connected in series with an inductor and an AC source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor ? Explain.

Q.

Electric power station 100 MW transmits power to a distant load through long and thin cables which of the following modes of transmission would result in less power wastage

A) 20, 000 V

B) 200 V

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. $45W$
4. $45\sqrt{2}W$
   

Q.

A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 μF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

Q.

A coil has a resistance of $10\Omega$ and an inductance of 0.4 henry. It is connected to an AC source of 6.5 V, $\frac{30}{\pi }$ Hz. Find the average power consumed in the circuit.

Q. For the circuit diagram shown, capacitive reactance $X_C=100\Omega ,$ inductive reactance $X_L=200\Omega$ and Resistance $R=100\Omega$. The effective current through the ac source of $200V$ is $\sqrt{N}$, then $N$ is

Q.

The peak power consumed by a resistive coil when connected to an AC source is 80 W. Find the enrgy consumed by the coil in 100 seconds which many times larger than the time period of the source.

Q. Seawater at a frequency $f=9\times {10}^2\text{Hz}$, has permittivity $\epsilon =80{\epsilon }_0$ and resistivity $\rho =0.25\Omega \text{m}$. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source $V\left(t\right)=V_0\sin \left(2\pi ft\right)$. Then, the conduction current between the plates becomes ${10}^x$ times the displacement current after time $t=1/800\text{s}$. The value of $x$ (integer only) is

Q. At a hydroelectric power plant, the water pressure head is at a heightof 300 m and the water flow available is 100 m3s–1. If the turbinegenerator efficiency is 60%, estimate the electric power availablefrom the plant (g = 9.8 ms–2 ).

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. A voltage $V=V_{0}sin\omega t$ is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle. Under what condition is
(i) no power dissipated even though the current flows through the circuit,
(ii) maximum power dissipated in the circuit?

Q. A direct current of $4\text{A}$ and an alternating current of peak value $4\text{A}$ flow through resistance of $3\Omega \text{and}2\Omega$ respectively. The ratio of heat produced in the two resistances in same interval of time will be

Q. The potential difference across an instrument in an a.c. circuit of frequency f is $V$ and the current flowing through it is $I$ such that $V=5\cos \left(2\pi ft\right)\text{volts}$ and $I=2\sin \left(2\pi ft\right)\text{amp}$. The power dissipate in the instrument is :

1. $10\text{watt}$
2. $5\text{watt}$
3. $2.5\text{watt}$
4. zero

Q. A parallel plate capacitor of capacitance 100 microfarad is connected to a power supply of 200V. A di-electric slab of dielectric constant 5 is now inserted into gap. The work done by the supply during this process is?

Q. For an ac circuit $V=15sin\omega t$ and $I=20cos\omega t$ the average power consumed in this circuit is

1. 300 Watt
2. 150 Watt
3. 75 Watt
4. zero

Q.

In an $\mathrm{A}.\mathrm{C}.$ circuit, the instantaneous e.m.f. and current are given by $\mathrm{e}=100\sin 30\mathrm{t}$ and $\mathrm{i}=20\sin \left(30\mathrm{t}-\left(\frac{\mathrm{\pi }}{4}\right)\right)$. In one cycle of $\mathrm{A}.\mathrm{C}.$, the average power consumed by the circuit and the wattles current are, respectively:

1. $\left(\frac{50}{\sqrt{2}},0\right)$

2. $50,0$

3. $50,10$

4. $\left(\frac{1000}{\sqrt{2}},10\right)$

Q. In an AC circuit , the current is given by 1= 4 sin(100 $\pi$ +300) ampere. The current becomes maximum first time (after t=0) at t equal to

1. $300sec$
2. $\left(1/300\right)sec$
3. $\left(1/50\right)sec$
4. $\left(1/200\right)sec$