Solution:

Ans. (i) Try yourself similar Q. 5 Long Answer Type Question.

(ii) Power factor :

$$ \begin{array}{rlr} P_{1} & =\frac{R}{Z}=\frac{R}{\sqrt{R^{2}+R^{2}}} \quad\left(\text { as } X_{L}=R\right) \ & =\frac{1}{\sqrt{2}} & 1 / 2 \end{array} $$

Power factor when capacitor $C$ of Reactance $X_{C}=$ $X_{L}$ is put in series in the circuit

$$ \begin{array}{rlr} Z & =R & \text { (at resonance) } \ P_{2} & =\frac{R}{Z}=\frac{R}{R}=1 & \ \therefore \quad & \frac{P_{1}}{P_{2}} & =\frac{\frac{1}{\sqrt{2}}}{n}=\frac{1}{\sqrt{2}} \end{array} $$

[CBSE Marking Scheme 2016]

[AI Q. 7. (i) With the help of a diagram, explain the principle and working of a device which produces current that reverses its direction after regular interyals of time.

(ii) If a charged capacitor $C$ is short circuited through an inductor $L$, the charge and current in the circuit oscillate simple harmonically.

(a) In what form the capacitor and the inductor store energy?

(b) Write two reasons due to which the oscillations become damped.

R [CBSE SQP 2015]

OR

(i) Figure shows the variation of resistance and reactance versus angular frequency. Identify the curve which corresponds to inductive reactance and resistance.

(ii) Show that series LCR circuit at resonance behaves as a purely resistive circuit. Compare the phase relation between current and voltage in series LCR circuit for (i) $X_{L}>X_{C}$ (ii) $X_{L}=X_{C}$ using phasor diagrams.

(iii) What is an acceptor circuit and where it is used ?

U] [CBSE SQP 2015]

Ans. (i) AC generator

Diagram

1

Principle

1

Working

1

(ii) (a) Capacitor - electric field Inductor - magnetic field

(b) resistance of the circuit

Radio tuning

Radiation in the form of EM waves

$1 / 2$

OR

(i) $B$ : inductive reactance

$C$ : resistance

(ii) At resonance $X_{L}=X_{C}$

Increase

$Z=\left[\left(X_{L}-X_{C}\right)^{2}+R^{2}\right]^{1 / 2}, Z=R$

Phasor diagrams

phase difference is $\phi$

for $\quad X_{L}>X_{C} \Rightarrow V_{L}>V_{C}$

same phase, i.e. $\phi=0$

(iii) Acceptor circuit : Series LCR circuit Radio tuning

Detailed Answer :

(i) $\mathrm{AC}$ generator

Basic elements of an $\mathrm{AC}$ generator :

• Rectangular coil : Also called as armature
• Strong permanent magnets : Magnetic field is perpendicular of the axis of rotation of coil.
• Slip rings
• Brushes

Rotation of coil

Field Motion Armature coil clockwise

AC generator

Principle : It is based on the principle of electromagnetic induction. That is, when a coil is rotated about an axis perpendicular to the direction of uniform magnetic field, an induced emf is produced across it.

Working of AC Generator

(ii) (a) The capacitor stores energy in the form of electric field and the inductor stores energy in the form of magnetic field.

(b) Oscillations become damped due to : $1 / 2+1 / 2$

• Resistance of the circuit
• Radiation in the form of EM waves $1 / 2$ OR

(i) Curve $B$ corresponds to inductive reactance and curve $C$ corresponds to resistance. $1 / 2+1 / 2$ (ii) At resonance,

$$ \begin{equation*} X_{L}=X_{C} \tag{1} \end{equation*} $$

Therefore, impedance is given as :

$$ \begin{aligned} & Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}} \ & Z=R \end{aligned} $$

Thus, series $L C R$ circuit at resonance behaves as a purely resistive circuit.

For $X_{L}>X_{C}, V_{L}>V_{C}$. Therefore phasor diagram is :

Here, $\phi$ is phase difference.

For $X_{L}=X_{C}, V_{L}=V_{C}$. Therefore phasor diagram is :

(iii) Series resonance $L C R$ circuit is called an acceptor circuit.

They are widely used in the tuning mechanism of a radio or a TV.