Alternating Current · Question 43

In an a.c. circuit the e.m.f. ( ) and the current (i) at any instant are given respectively by = E0 sin t, i = I0 sin( t - ) The average power in the circuit over one cycle of a.c. is

1. E0I02
2. E0I0
3. E0I02
4. E0I02

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux linked with the primary coil is given by = 0 + 4t, where is in webers, t is time in seconds and 0 is a constant, the output voltage across the secondary coil is

1. 120 volt
2. 220 volts
3. 30 volts
4. 90 volts

A transformer is used to light a 100 W and 110 V lamp from a 220 V mains. If the main current is 0.5 amp, the efficiency of the transformer is approximately

1. 50%
2. 90%
3. 10%
4. 30%

What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10 F and = 1000 s-1 ?

1. 1 mH
2. cannot be calculated unless R is known
3. 10 mH
4. 100 mH

A coil of inductive reactance 31 has a resistance of 8 . It is placed in series with a condenser of capacitative reactance 25 . The combination is connected to an a.c. source of 110 V. The power factor of the circuit is

1. 0.33
2. 0.56
3. 0.64
4. 0.80

The core of a transformer is laminated because

1. ratio of voltage in primary and secondary may be increased
2. energy losses due to eddy currents may be minimised
3. the weight of the transformer may be reduced
4. rusting of the core may be prevented.

A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produces oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be

1. f/2
2. f/4
3. 8f
4. f/2 2

In a circuit L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45 . The value of C is

1. 1 f(2 fL - R)
2. 12 f(2 fL - R)
3. 1 f(2 fL + R)
4. 12 f(2 fL + R)

For a series LCR circuit the power loss at resonance is

1. V2 [ L - 1 C ]
2. I2L
3. I2R
4. V2C

A capacitor of capacity C has reactance X. If capacitance and frequency become double then reactance will be

1. 4X
2. X/2
3. X/4
4. 2X