a series RLC circuit is composed of a 6.00-mH inductor and a 2.50-uF capacitor. what is the resonant frequency of this circuit?
The resonance frequency is
1/((LC)^0.5)
Where L is the inductance = 6 * 10 ^-3 H
and C is the capacitance = 2.5 * 10^-6 F
To find the resonant frequency of a series RLC circuit, you can use the formula:
Resonant frequency (f) = 1 / (2π√(LC))
Where:
L is the inductance of the inductor (in henries).
C is the capacitance of the capacitor (in farads).
π is a mathematical constant approximately equal to 3.14159.
Now let's calculate the resonant frequency of the given series RLC circuit:
Given:
L = 6.00 mH = 6.00 × 10^(-3) H (since 1 mH = 10^(-3) H)
C = 2.50 μF = 2.50 × 10^(-6) F (since 1 μF = 10^(-6) F)
Using the formula:
f = 1 / (2π√(LC))
Substituting the given values:
f = 1 / (2π√((6.00 × 10^(-3)) * (2.50 × 10^(-6))))
Now let's calculate this using a calculator:
f = 1 / (2 * 3.14159 * √((6.00 × 10^(-3)) * (2.50 × 10^(-6))))
f ≈ 1 / (2 * 3.14159 * 0.00387)
f ≈ 1 / (6.12395 * 0.00387)
f ≈ 1 / 0.023722
f ≈ 42.177 Hz
Therefore, the resonant frequency of the given series RLC circuit is approximately 42.177 Hz.