SATHEE: alternating-currents Question 18

alternating-currents Question 18

Question: Q. 2. (i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase : current or voltage?

(ii) Without making any other change, find the value of the additional capacitor $C_{1}$ , to be connected in parallel with the capacitor $C$ , in order to make the power factor of the circuit unity.

U] [Delhi I, II, III 2017]

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Solution:

Ans. (i) Calculation of phase difference between current and voltage

Name of quantity which leads

(ii) Calculation of value of ’ $C$ ‘, is to be connected in parallel

(i) $X_{L} = ω L = (1000 \times 100 \times 10^{- 3}) Ω$

$= 100 Ω$

$X_{C} = \frac{1}{ω C} = (\frac{1}{1000 \times 2 \times 10^{- 6}}) Ω$

$= 500 Ω$

Phase angle

$\begin{aligned} \tan ϕ & = \frac{X_{L} - X_{C}}{R} \tan ϕ & = \frac{100 - 500}{400} = - 1 ϕ & = - \frac{π}{4} \end{aligned}$

As $X_{C} > X_{L}$ (phase angle is negative), hence current leads voltage (ii) To make power factor unity

$\begin{aligned} X_{C^{'}} & = X_{L} \frac{1}{ω C^{'}} & = 100 C^{'} & = 10 μ F C^{'} & = C + C_{1} 10 & = 2 + C_{1} C_{1} & = 8 μ F \end{aligned}$

[CBSE Marking Scheme 2017]

[AI Q. 3. A sinusoidal voltage of peak value $10 V$ is applied to a series $L C R$ circuit in which resistance, capacitance and inductance have values of $10 Ω$ , $1 μ F$ and $1 H$ respectively. Find (i) the peak voltage across the inductor at resonance (ii) quality factor of the circuit.

U] [CBSE SQP 2018-19]

Ans.

$I_{0} = V_{0} / R = 10 / 10 = 1 A 1 / 2$

$ω_{r} = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{(1 \times 1 \times 10^{- 6})}}^{1 / 2}$

$= 10^{3} rad / s$

$V_{0} = I_{0} X_{L} = I_{0} ω_{r} L$

$= 1 \times 10^{3} \times 1 = 10^{3} V$

$Q = ω_{r} L / R$

$= (10^{3} \times 1) / 10 = 100 1 / 2$

[CBSE Marking Scheme 2018]

Alternating Currents

alternating-currents Question 18

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Alternating Currents

alternating-currents Question 18

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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