Alternating Current

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