Alternating Current · Question 8

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