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

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

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

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

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 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