Alternating Current

An ac circuit contains a resistance of 1 kΩ, a capacitor of 0.1 μF and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately :

1. 15.9 kHz
2. 20.7 kHz
3. 10.1 kHz
4. 13.5 kHz

The peak value of an alternating current is 5 A and frequency is 60 Hz. How long will the current, starting from zero, take to reach the peak value ?

1. 1120 s
2. 1240 s
3. 130 s
4. 160 s

An ac voltage V = 220 (2 103 t) Volt is applied to a series LCR circuit. Then the current amplitude in this circuit is: (Given : L = 10 mH, C = 25 , R = 100 )

1. 22.0 A
2. 2.2 A
3. 5.5 A
4. 11.0 A

To an ac power supply of 220 V at 50 Hz, a resistor of 20 , a capacitor of reactance 25 and an inductor of reactance 45 are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively

1. 15.6 A and 30
2. 15.6 A and 45
3. 7.8 A and 30
4. 7.8 A and 45

In an ideal transformer, the turns ratio is NPNS = 12. The ratio VS : VP is equal to (the symbols carry their usual meaning) :

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

A 10 capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly ( = 3.14) : [figure]

1. 0.58 A
2. 0.93 A
3. 1.20 A
4. 0.35 A

In the circuit shown below, the inductance L is connected to an ac source. The current flowing in the circuit is I = I0 t. The voltage drop (VL) across L is [figure]

1. L I0 t
2. I0 L t
3. I0 L t
4. L I0 t

A step up transformer is connected to an ac mains supply of 220 V to operate at 11000 V, 88 watt. The current in the secondary circuit, ignoring the power loss in the transformer, is

1. 8 mA
2. 4 mA
3. 0.4 A
4. 4 A

The amplitude of the charge oscillating in a circuit decreases exponentially as Q = Q0e-Rt/2L, where Q0 is the charge at t = 0 s. The time at which charge amplitude decreases to 0.50Q0 is nearly: [Given that R = 1.5 , L = 12 mH, (2) = 0.693]

1. 19.01 ms
2. 11.09 ms
3. 19.01 s
4. 11.09 s

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 and resistance R is 100 . The frequency at which resonance occurs is :-

1. 15.9 kHz
2. 1.59 rad/s
3. 1.59 kHz
4. 15.9 rad/s

A 12 V, 60 W lamp is connected to the secondary of a step down transformer, whose primary is connected to ac mains of 220 V. Assuming the transformer to be ideal, what is the current in the primary winding?

1. 2.7 A
2. 3.7 A
3. 0.37 A
4. 0.27 A

An ac source is connected to a capacitor C. Due to decrease in its operating frequency :

1. displacement current increases.
2. displacement current decreases.
3. capacitive reactance remains constant.
4. capacitive reactance decreases.

The net impedance of circuit (as shown in figure) will be : [figure]

1. 15
2. 5 5
3. 25
4. 10 2

The peak voltage of the ac source is equal to

1. The value of voltage supplied to the circuit
2. The rms value of the ac source
3. 2 times the rms value of the ac source
4. 1/ 2 times the rms value of the ac source

A series LCR circuit with inductance 10 H, capacitance 10 , resistance 50 is connected to an ac source of voltage, V = 200 (100t) volt. If the resonant frequency of the LCR circuit is 0 and the frequency of the ac source is , then

1. 0 = = 50 Hz
2. 0 = = 50 Hz
3. 0 = 50 Hz, = 50 Hz
4. = 100 Hz, 0 = 100 Hz

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

1. Statement I is incorrect but Statement II is correct
2. Both Statement I and Statement II are correct
3. Both Statement I and Statement II are incorrect
4. Statement I is correct but Statement II is incorrect

An inductor of inductance 2 mH is connected to a 220 V, 50 Hz ac source. Let the inductive reactance in the circuit is X1. If a 220 V dc source replace the ac source in the circuit, then the inductive reactance in the circuit is X2. X1 and X2 respectively are :

1. 0.628 , infinity
2. 6.28 , zero
3. 6.28 , infinity
4. 0.628 , zero

A standard filament lamp consumes 100 W when connected to 200 V ac mains supply. The peak current through the bulb will be :

1. 2 A
2. 0.707 A
3. 1 A
4. 1.414 A

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference 'V' volts as shown in figure. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10 2 A. The impedance of the circuit is : [figure]

1. 5
2. 4 2
3. 5/ 2
4. 4

A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit ?

1. 4 A
2. 0.2 A
3. 0.4 A
4. 2 A

A series LCR circuit containing 5.0 H inductor, 80 F capacitor and 40 resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be :

1. 42 rad/s and 58 rad/s
2. 25 rad/s and 75 rad/s
3. 50 rad/s and 25 rad/s
4. 46 rad/s and 54 rad/s

A 40 capacitor is connected to a 200 V, 50 Hz ac supply. The rms value of the current in the circuit is, nearly :

1. 2.05 A
2. 2.5 A
3. 25.1 A
4. 1.7 A

A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is 3. If instead C is removed from the circuit, the phase difference is again 3 between current and voltage. The power factor of the circuit is :

1. 0.5
2. 1.0
3. -1.0
4. zero

An inductor 20 mH, a capacitor 100 and a resistor 50 are connected in series across a source of emf, V = 10 314 t. The power loss in the circuit is

1. 0.79 W
2. 0.43 W
3. 2.74 W
4. 1.13 W

An inductor 20 mH, a capacitor 50 and a resistor 40 are connected in series across a source of emf V = 10 340t. The power loss in A.C. circuit is

1. 0.76 W
2. 0.89 W
3. 0.46 W
4. 0.67 W

A small signal voltage V(t) = V0 t is applied across an ideal capacitor C

1. Current I(t) is in phase with voltage V(t).
2. Current I(t) leads voltage V(t) by 180
3. Current I(t) lags voltage V(t) by 90 .
4. Over a full cycle the capacitor C does not consume any energy from the voltage source.

Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication?

1. R = 20 , L = 1.5 H, C = 35
2. R = 25 , L = 2.5 H, C = 45
3. R = 15 , L = 3.5 H, C = 30
4. R = 25 , L = 1.5 H, C = 45

The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is

1. 0.4
2. 0.5
3. 0.8
4. 1.0

A series R-C circuit is connected to an alternating voltage source. Consider two situations : (a) When capacitor is air filled. (b) When capacitor is mica filled. Current through resistor is i and voltage across capacitor is V then

1. ia > ib
2. Va = Vb
3. Va < Vb
4. Va > Vb

A resistance 'R' draws power 'P' when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes 'Z', the power drawn will be

1. P ( RZ )
2. P
3. P ( RZ )2
4. P RZ