SATHEE: alternating-currents Question 21

alternating-currents Question 21

Question: Q. 7. The current, in the $L C R$ circuit shown in the figure is observed to lead the voltage in phase. Without making any other change in the circuit, a capacitor, of capacitance $C_{0}$ , is (appropriately) joined to the capacitor $C$ . This results in making the current, in the ‘modified’ circuit, flow in phase with the applied voltage.

Draw a diagram of the ‘modified’ circuit and obtain an expression for $C_{0}$ in terms of $ω, L$ and $C$ .

] [Foreign 2016]

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Solution:

Ans. The current leads the voltage in phase. Hence, $X_{c} > X_{L}$

For resonance, we must have

$1 / 2$

New value of $X_{c} = X_{L}$

We, therefore, need to decrease $X_{c} = (\frac{1}{ω C})$ . This requires an increase in the value of $C$ . Hence, capacitor $C_{0}$ should be connected in parallel across C. $1 / 2$ The diagram of the modified circuit is as shown.

For resonance, we have

$\begin{aligned} \frac{1}{ω (C + C_{0})} & = ω L C_{0} & = [\frac{1}{ω^{2} L} - C] \end{aligned}$

[CBSE Marking Scheme 2016]

Alternating Currents

alternating-currents Question 21

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Alternating Currents

alternating-currents Question 21

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

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