The variation of the instantaneous current $(I)$ and the instantaneous emf $(E)$ in a circuit are shown in the figure. Which of the following statements is correct?

The figure shows the variation of R, X_L, and X_C with frequency f in a series L, C, R circuit. Then for what frequency point, the circuit is inductive:

1. A

2. B

3. C

4. All points

An ac source of variable frequency f is connected to an LCR series circuit. Which one of the graphs in the figure represents the variation of the current I in the circuit with frequency f :

1. 

2. 

3. 

4. 

The potential differences across the resistance, capacitance and inductance are $80$ V, $40$ V and $100$ V respectively in an $LCR$ circuit. What is the power factor of this circuit?
1. $0.4$
2. $0.5$
3. $0.8$
4. $1.0$

An inductor 20 mH, a capacitor 50μF, and a resistor 40Ω are connected in series across a source of emf V=10sin340t. The power loss in the AC circuit is:

1. 0.67 W

2. 0.78W

3. 0.89 W

4. 0.46 W

A series R-C circuit is connected to an alternating voltage source. Consider two situations:

(1) When the capacitor is air-filled.

(2) When the capacitor is mica filled.

Current through the resistor is I and voltage across the capacitor is V then

1. V_a<V_b
 

2. V_a>V_b
 

3. i_a>i_b
 

4. V_a=V_b

The instantaneous values of alternating

current and voltages in a circuit are given

as 

$\mathrm{i}=\frac{1}{\sqrt{2}}\sin \left(100\mathrm{\pi t}\right) \mathrm{ampere}$
$\mathrm{e}=\frac{1}{\sqrt{2}}\sin (100\mathrm{\pi t}+\mathrm{\pi }/3) \mathrm{volt}$

The average power in Watts consumed in the

circuit is

1. $\frac{1}{4}$

2. $\frac{\sqrt{3}}{4}$

3. $\frac{1}{2}$ 

4. $\frac{1}{8}$

In an AC circuit an alternating voltage $\mathrm{e}=200 \sqrt{2} \sin 100\mathrm{t}$ volt is connected to a capacitor $1 \mathrm{\mu F}.$ The $\mathrm{rms}$ value of the current in the circuit is

(a) 100 mA

(b) 200 mA

(c) 20 mA

(d) 10 mA

In AC circuit the emf (e) and the current (i) at any instant are given respectively by

$e=E_o \sin \omega t$

$i=I_o\sin (\omega t-\varphi )$

The average power in the circuit over one cycle of AC is 

1.$\frac{E_o{I}_o}{2}$

2. $\frac{E_o{I}_o}{2}\sin \varphi$

3. $\frac{E_o{I}_o}{2}\cos \varphi$

4. $E_o{I}_o$