Question

In a series LCR circuit l equal to 8 X equal to 0.5 microfarad and are equal to 100 ohm the resonant frequency of the circuit is

Answer 1

We know, L and C impedances are equal but in opposite sign.
e.g., Xl = Xc
here, represents impedance of inductance
And represents impedance of capacitance
∴ XL = ωC
Xc = 1/ωL
1/ωL = ωC
ω² = 1/Lc
So , ω = 1/√Lc
1/2π√LC
Hence, resonant frequency =
Now, put L = 8H and C = 0.5μF = 5 × 10⁻⁶ F
then, f = 79.57 Hz