SATHEE: alternating-currents Question 23

Alternating Currents

alternating-currents Question 23

Question: Q. 11. A source of $a c$ voltage $V = V_{0} \sin ω t$ is connected to a series combination of a resistor ’ $R$ ’ and a capacitor ’ $C$ ‘. Draw the phasor diagram and use it to obtain the expression for (i) impedance of the circuit and (ii) phase angle. U] [O.D. I, II, III 2015]

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Solution:

Ans. The Pythagoras theorem gives

$V_{m}^{2} = V_{r m}^{2} + V_{c m}^{2}$

Substituting the values of $V_{r m}$ and $V_{c m}$ into this equation, gives

$\begin{aligned} V_{m}^{2} & = {(i_{m} R)}^{2} + {(i_{m} X_{C})}^{2} & = i_{m}^{2} (R^{2} + X_{C}^{2}) i_{m} & = \frac{V_{m}}{\sqrt{R^{2} + X_{C}^{2}}} \end{aligned}$

$∴$ The impedance of the circuit is given by :

$Z = \sqrt{R^{2} + X_{C}^{2}} = \sqrt{R^{2} + \frac{1}{ω^{2} C^{2}}}$

The phase angle is the angle between $V_{R}$ and $V$ . Hence

$\tan ϕ = \frac{X_{C}}{R} = \frac{1}{ω C R}$

$1 / 2$

The circuit diagram and the phasor diagram, for the given circuit, are as shown.

Alternating Currents

alternating-currents Question 23

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Alternating Currents

alternating-currents Question 23

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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