A bulb is rated at \(100\) V, \(100\) W, and is treated as a resistor. The inductance of an inductor (choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an AC source of \(200\) V and \(50\) Hz is:
1. \(\dfrac{\pi }{\sqrt{3}}~\text{H}\)
2. \(100~\text{H}\)
3. \(\dfrac{\sqrt{2}}{\pi }~\text{H}\)
4. \(\dfrac{\sqrt{3}}{\pi }~\text{H}\)

The value of current in two series LCR circuit at resonance is the same when connected across a sinusoidal voltage source. Then

1. Both circuit should have the same value of capacitance and inductor

2. In both circuits, the ratio of L and C will be the same

3. For both the circuits, resistance must be the same

4. Both circuit should have the same impedance at all frequencies

An ideal transformer is made to step down the power line voltage of 2200 V for distribution to a city at 220 v. If the full load impedance of the city is 4 $\Omega$ then the primary current is

1. 45 A

2. 5.5 A

3. 55 A

4. 0.55 A

What is the phase difference between potential difference across the inductor and potential difference across the capacitor in a series LCR circuit?

1. Zero

$2. \frac{\pi }{4}$
$3. \frac{\pi }{4}$
$4. \pi$

For a series, LCR circuit quality factor is $\alpha$ and potential difference across circuit $\beta$. The potential difference across the inductor in resonance state will be:

1. Zero

2. $\alpha \beta$

3. $\frac{\beta }{\alpha }$

4. $\frac{\alpha }{\beta }$

The ratio of current delivered by the battery just after the switch is closed to a long time after the switch closed is

 $1. \frac{2}{3}$
$2. \frac{5}{6}$
$3. \frac{3}{2}$
$4. \frac{3}{4}$

What is the reading of the A.C voltmeter in the network as shown in the figure?

1. zero

2. 100 V

3. 200 V

4. 400 v

What is the value of the power factor for a parallel LC circuit at a frequency less than the resonance frequency?

1. Zero

2. 1

3. > 1

4.< 1

When an alternating voltage is given as; \(E = (6 \sin\omega t - 2 \cos \omega t)~\text V,\) what is its RMS value?
1. \(4 \sqrt 2 ~\text V\) 
2. \(2 \sqrt 5 ~\text V\) 
3. \(2 \sqrt 3 ~\text V\) 
4. \(4 ~\text V\) 

Current through an elements in ac circuit is said to be wattless, when the elements is

1. Pure inductor (L)

2. Pure capacitor (C)

3. Series L-C circuit

4. All of these