Alternating Current

A LCR series circuit driven with Erms=90 V at frequency fd=30 Hz has resistance R=80 , an inductance with inductive reactance XL=20.0 and capacitance with capacitive reactance XC=80.0 . The power factor of the circuit is .

1. 0.8
2. 0.64
3. 0.9
4. 0.5

An a.c. source of angular frequency is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the source is changed to /4, (keeping the voltage unchanged) the current is found to be I/3. The ratio of resistance to reactance at frequency is

1. 67
2. 35
3. 78
4. 34

A series LCR circuit with R=20 , L=1.6 H and C=40 F is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is .

An inductor of 10 mH, capacitor of 0.1 μF and a resistor of 100 Ω are connected in series across an a.c. power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitive reactance is 3 Ω. The value of is .

The figure given below shows an LCR series circuit with two switches S1 and S2. When switch S1 is closed keeping S2 open, the phase difference ( ) between the current and source voltage is 30° and phase difference is 60° when S2 is closed keeping S1 open. The value of (3L1-L2) is H. [figure]

1. 92
2. 29
3. 13
4. 3

The electric current in the circuit is given as i = io(t/T). The r.m.s current for the period t = 0 to t = T is .

1. io 2
2. io 3
3. io
4. io 6

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is . ( = 3.14)

For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is 10. The value of is . [figure]

1. 4
2. 8
3. 6
4. 10

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5 (100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is . [figure]

A capacitor C is first charged fully with potential difference of V0 and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In t s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is s.

1. LC3
2. LC2
3. LC2
4. LC6

An ac current is represented as i = 5 2 + 10 (650 t + 6 ) Amp The r.m.s. value of the current is

1. 10 Amp
2. 5 2 Amp
3. 100 Amp
4. 50 Amp

For ac circuit shown in figure, R = 100 k and C = 100 pF and the phase difference between Vin and (VB - VA) is 90 . The input signal frequency is 10x rad/sec, where 'x' is . [figure]

An inductor of reactance 100 , a capacitor of reactance 50 , and a resistor of resistance 50 are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is W.

An alternating current is represented by the equation, i = 100 2 (100 t) ampere. The RMS value of current and the frequency of the given alternating current are

1. 100 2 A, 100 Hz
2. 50 2 A, 50 Hz
3. 100 2 A, 100 Hz
4. 100 A, 50 Hz

An inductor of self inductance 1 H is connected in series with a resistor of 100 ohm and an ac supply of 100 volt, 50 Hz. Maximum current flowing in the circuit is A.

An electric bulb rated as 100 W - 220 V is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is:

1. 0.32 A
2. 0.64 A
3. 0.45 A
4. 2.2 A

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below :

1. (A) is true but (R) is false
2. Both (A) and (R) are true and (R) is the correct explanation of (A).
3. Both (A) and (R) are true but (R) is not the correct explanation of (A)
4. (A) is false but (R) is true

An alternating current is given by I=IA t+IB t. The r.m.s current will be

1. IA2+IB22
2. IA2+IB22
3. |IA+IB| 2
4. IA2+IB2

In a series LCR circuit, a resistor of 300 , a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is 104 radians s-1

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I0. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

1. I02
2. I0 2
3. 2I0
4. I0