When 100 volt d.c. is applied across a solenoid, a current of 1.0 A flows in it. When 100 volt a.c. is appliead across the same coil, the current drops to 0.5 A. If the frequency of a.c. source is 50 Hz the impedance and inductance of the solenoid is

1. 200 $\mathrm{\Omega }$ and 0.55 H

2. 100 $\mathrm{\Omega }$ and 0.86 H

3. 200 $\mathrm{\Omega }$ and 1.0 H

4. 100 $\mathrm{\Omega }$ and 0.93 H

In a series RLC circuit, potential differences across R, L and C are 30 V, 60 V and 100 V respectively, as shown in the figure. The emf of the source (in volts) will be:

1. 190

2. 70

3. 50

4. 40

In a series LCR circuit, the phase difference between voltage across L and voltage across C is equal to:

When does the voltage in a series LCR circuit lead the current? (Given that ${\mathrm{\omega }}_0=$resonant angular frequency)

1. $\mathrm{\omega }<{\mathrm{\omega }}_0$

2. $\mathrm{\omega }={\mathrm{\omega }}_0$

3. $\mathrm{\omega }>{\mathrm{\omega }}_0$

4. None of these

The reactance of a circuit is zero. It is possible that the circuit contains:

1. an inductor and a capacitor

2. an inductor but no capacitor

3. a capacitor but no inductor

4. All of the above

In the given figure, a lamp P is in series with an iron-core inductor L. When the switch S is closed, the brightness of the lamp rises relatively slowly to its full brightness than it would do without inductor in circuit. This is due to:

1. the low resistance of P

2. the induced emf in L

3. the low resistance of L

4. the low voltage of the battery B

In a series R-L-C circuit, the frequency of the source is half of the resonance frequency. The name of the circuit will be:

1. capacitive

2. inductive

3. purely resistive

4. data insufficient

The time required for a 50 Hz sinusoidal alternating current to change its value from zero to the r.m.s. value will be:

1. $1.5\times {10}^{-2}$ $\mathrm{s}$

2. $2.5\times {10}^{-3}$ $\mathrm{s}$

3. ${10}^{-1}$ $\mathrm{s}$

4. ${10}^{-6}$ $\mathrm{s}$

A simple electric motor has an armature resistance of $1\mathrm{\Omega }$ and runs from a d.c. source of 12 V. It draws a current of 2 A when unloaded. When a certain load is connected to it, its speed reduces by 10% of its initial value. The current drawn by the loaded motor is

1. 3 A

2. 6 A

3. 2 A

4. 1 A

What is the Q-factor of a series LCR circuit with L = 3.0 H, C = 27µF, and R = 7.4 Ω?

1. 45
2. 55
3. 37
4. 49