For a given series LCR circuit it is found that maximum current i… - Vidyadip

MCQ

For a given series $LCR$ circuit it is found that maximum current is drawn when value of variable capacitance is $2.5 \mathrm{nF}$. If resistance of $200 \Omega$ and $100 \mathrm{mH}$ inductor is being used in the given circuit. The frequency of ac source is . . . . $\times 10^3 \mathrm{~Hz}$. (given $\pi^2=10$ )

A
$9$
✓
$10$
C
$11$
D
$12$

✓

Answer

Correct option: B.

$10$

b
b
for maximum current, circuit must be in resonance

$\mathrm{f}_0=\frac{1}{2 \pi \sqrt{\mathrm{L} \times \mathrm{C}}}$

$\mathrm{f}_0=\frac{1}{2 \pi \sqrt{100 \times 10^{-3} \times 2.5 \times 10^{-9}}}$

$=\frac{1}{2 \pi \sqrt{25 \times 10^{-11}}}$

$=\frac{1}{2 \pi \times 5} \times 10^5 \times \sqrt{10} \mathrm{~Hz}$

$=\frac{100}{10} \times 10^3 \mathrm{~Hz}$

$\mathrm{f}_0=10 \times 10^3 \mathrm{~Hz}$

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