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

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

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

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

1. becomes zero
2. remains same
3. increases
4. decreases

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

1. halved
2. same
3. Zero
4. double

A coil of negligible resistance is connected in series with 90 resistor across 120 V, 60 Hz supply. A voltmeter reads 36 V across resistance. Inductance of the coil is :

1. 0.91 H
2. 0.76 H
3. 2.86 H
4. 0.286 H

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is true but Statement II is false
2. Statement I is false but Statement II is true
3. Both Statement I and Statement II are true
4. Both Statement I and Statement II are false

A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is .

1. 10 A
2. 10 mA
3. 68 A
4. 63 A

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : Choose the correct answer from the options given below :

1. A, B and C only
2. A and B only
3. A, B and D only
4. B, C and D only

In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be:

1. increased by 2 L
2. reduced by 14 L
3. reduced by 34 L
4. increased to 4 L

A transformer has an efficiency of 80\% and works at 10 V and 4 kW. If the secondary voltage is 240 V, then the current in the secondary coil is :

1. 1.33 A
2. 13.33 A
3. 1.59 A
4. 15.1 A

An AC voltage V=20 200 t is applied to a series LCR circuit which drives a current I=10 (200 t+ 3 ). The average power dissipated is:

1. 21.6 W
2. 200 W
3. 173.2 W
4. 50 W

Primary coil of a transformer is connected to 220 V ac. Primary and secondary turns of the transformer are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistances shown in figure. The output voltage (V0) is : [figure]

1. 7 V
2. 44 V
3. 22 V
4. 15 V

A series L.R circuit connected with an ac source E=(25 1000t) V has a power factor of 1 2. If the source of emf is changed to E=(20 2000t) V, the new power factor of the circuit will be :

1. 1 3
2. 1 2
3. 1 5
4. 1 7

An alternating voltage V(t)=220 100 t volt is applied to a purely resistive load of 50 . The time taken for the current to rise from half of the peak value to the peak value is:

1. 7.2 ms
2. 3.3 ms
3. 5 ms
4. 2.2 ms

A capacitor of capacitance 100 is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be :

1. 2.0 A
2. 3.2 A
3. 1.5 A
4. 1.2 A

In an a.c. circuit, voltage and current are given by: V=100 (100t) V and I=100 (100t+ 3 )mA respectively. The average power dissipated in one cycle is:

1. 5 W
2. 25 W
3. 2.5 W
4. 10 W

Primary side of a transformer is connected to 230 V, 50 Hz supply. Turns ratio of primary to secondary winding is 10:1. Load resistance connected to secondary side is 46 . The power consumed in it is :

1. 11.5 W
2. 12.5 W
3. 10.0 W
4. 12.0 W