SATHEE: alternating-currents Question 31

alternating-currents Question 31

Question: Q. 8. (i) A series $L C R$ circuit is connected to an ac source of variable frequency. Draw a suitáble phasor diagram to deduce the expressions for the amplitude of the current and phase angle.

(ii) Obtain the condition at resonance. Draw a plot showing the variation of current with the frequency of a.c. source for two resistances $R_{1}$ and $R_{2} (R_{1} > R_{2})$ . Hence define the quality factor, $Q$ and write its role in the tuning of the circuit.

U] [Delhi Comptt. I, II, III 2014]

Show Answer

Solution:

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

(ii) At resonance, $I_{m}$ is maximum.

$\Rightarrow X_{L} = X_{C^{'}}$

[Alternatively : $ω_{0} = \frac{1}{\sqrt{L C}}$ ]

(ii) plot is for $R_{1}$ (i) plot is for $\mathrm{R}{2}\left(R{2}>R_{1}\right)$

Quality factor of $L C R$ circuit is defined as

$\begin{matrix} (1) & \frac{ω_{0}}{2 Δ ω} = \frac{ω_{0} L}{R} \end{matrix}$

A larger value of quality factor corresponds to a sharper resonance.

[CBSE Marking Scheme, 2014]

Alternating Currents

alternating-currents Question 31

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Alternating Currents

alternating-currents Question 31

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu