Question

In a series L - C - R circuit, at what frequency does the inductive reactance of a $50\mu$ H inductor equals the reactance of a $200\mu F$ capacitor?

• A. 1000 Hz
• B. 1200 Hz
• C. 1400 Hz
• D. 1600 Hz

Answer 1

The correct option is D 1600 Hz

$f_0=\frac{1}{2\pi \sqrt{LC}}=\frac{1}{2\pi \sqrt{50\times {10}^{-6}\times 200\times {10}^{-6}}}$
$=\frac{1}{2\pi \sqrt{{10}^4\times {10}^{-12}}}=\frac{{10}^4}{2\pi }=\frac{5000}{\pi }Hz=1600Hz$