SATHEE: alternating-currents Question 28

Alternating Currents

alternating-currents Question 28

Question: Q. 3. (i) Prove that an ideal capacitor in an $a c$ circuit does not dissipate power.

(ii) An inductor of $200 mH$ , capacitor of $400 μ F$ and a resistor of $10 Ω$ are connected in series to ac source of $50 V$ of variable frequency. Calculate the

(a) angular frequency at which maximum power dissipation occurs in the circuit and the corresponding value of the effective current, and

(b) value of $Q$ -factor in the circuit.

A [O.D. Comptt I, II, III 2010 ]

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Solution:

Ans. (i) Average Power dissipation is zero

(ii) Numerical

(i) Try yourself, Similar to Q. 1, Short Answer Ihpe Questions-II

(ii) (a)

$\begin{aligned} ω_{0} & = \frac{1}{\sqrt{L C}} \times 1 & = \frac{1}{\sqrt{8 \times 10^{- 5}}} rad / s & = \frac{10^{3}}{\sqrt{80}} rad / s & ≅ 111 rad / s . \end{aligned}$

$I = \frac{V}{R} = \frac{50}{10} = 5 A$

(b)

$\begin{aligned} Q & = \frac{1}{R} \sqrt{\frac{L}{C}} & = \frac{1}{10} \sqrt{\frac{200 \times 10^{- 3}}{400 \times 10^{- 6}}} = \sqrt{5} \end{aligned}$

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Alternating Currents

alternating-currents Question 28

A [O.D. Comptt I, II, III 2010 ]

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Alternating Currents

alternating-currents Question 28

A [O.D. Comptt I, II, III 2010 ]

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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