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 $200 \mathrm{mH}$, capacitor of $400 \mu \mathrm{F}$ and a resistor of $10 \Omega$ are connected in series to ac source of $50 \mathrm{~V}$ 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)
$$ \begin{aligned} \omega_{0} & =\frac{1}{\sqrt{L C}} \times 1 \ & =\frac{1}{\sqrt{8 \times 10^{-5}}} \mathrm{rad} / \mathrm{s} \ & =\frac{10^{3}}{\sqrt{80}} \mathrm{rad} / \mathrm{s} \ & \cong 111 \mathrm{rad} / \mathrm{s} . \end{aligned} $$
$$ I=\frac{V}{R}=\frac{50}{10}=5 \mathrm{~A} $$
(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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