An L ? C circuit contains a single inductor in parallel with a single capacitor. The inductor has an inductance of 0.55 mH and the circuit has a resonant frequency of 250 kHz. What is the capacitance of the capacitor? I keep getting 2.9e-8, but the correct answer is 7.4e-10, and I have no idea why.
Resonating Frequency 1/(2π√LC) 250x10? 1/(2π√(0.55x10^-3)C) 250,000 1/(2π√(0.55x10^-3)C) 250000 x 2π 1/√(0.55x10^-3)C) √(0.55x10^-3)C) 1/(250000 x 2π) (0.55x10^-3)C) (1/(250000 x 2π))? C ≈ 7.4E-10 F
Inductors are also similar to resistors and add in series. There are two components in inductors, the resistance and inductance. The resistance is negligible compared to inductance. But inductance comes into play only when an alternating current flows. Inductance L x2 pi x f where L inductance, pi 3.14 and f frequency
Fr 1 / ((2 x pi) x (sq.rt.(L x C))) sq.rt. (L x C) 1 / ((2 x pi) x Fr) [square both sides of the equation] L x C 1 / ((2 x pi)^2 x (Fr)^2) Solve for C, C 1 / ((2 x pi)^2 x (Fr)^2 x L) C 1 / (6.28^2 x (2.5x10^5)^2 x 0.55 x 10^-3) C 1 / (39.4384 x 62500000000 x 0.00055) C 7.38 x 10^-10 farads, 0.000,000,000738 farads, or 738 pfd Plug C back into the original equation for Fr and see if you get the expected resonant frequency.
