a series RLC circuit is comprised of a 6.00-mH inductor and a 2.50-muiF capacitor. what is the resonant frequency of this circuit?
1/[2 pi sqrt(LC)]
To calculate the resonant frequency of an RLC circuit, you need to use the following formula:
Resonant frequency (f0) = 1 / (2π √(LC))
In this case, L represents the inductance, and C represents the capacitance.
Given:
Inductance (L) = 6.00 mH (millihenries)
Capacitance (C) = 2.50 μF (microfarads)
Step 1: Convert the units
Since the units of the inductor and the capacitor in the formula are different, we need to convert the values to be consistent with each other. Convert 6.00 mH to H by dividing by 1000.
L = 6.00 mH = 6.00 × 10^(-3) H
Also, convert 2.50 μF to F by dividing by 1,000,000.
C = 2.50 μF = 2.50 × 10^(-6) F
Step 2: Substitute the values into the formula
Now we can substitute the values into the resonant frequency formula:
f0 = 1 / (2π √(LC))
= 1 / (2π √(6.00 × 10^(-3) H × 2.50 × 10^(-6) F))
Step 3: Calculate the resonant frequency
Using a calculator or computer, perform the calculations to find the resonant frequency value:
f0 ≈ 1 / (2π √(6.00 × 10^-9 H × 2.50 × 10^-6 F))
≈ 1 / (2π √(1.5 × 10^-14 H.F))
≈ 1 / (2π × 3.87 × 10^-7 Hz)
≈ 1 / (7.72 × 10^-7 Hz)
≈ 1.30 × 10^6 Hz
Therefore, the resonant frequency of the RLC circuit is approximately 1.30 MHz (megahertz).