Question

in series LCR circuit L 8 c 0.5 uf R 100 ohm .the resonant frequency of circuit is

Answer 1

We know, L and C impedances are equal but in opposite sign.
e.g., $\bold{X_L = X_C}$
here, $\bold{X_L}$ represents impedance of inductance
And $\bold{X_C}$ represents impedance of capacitance
∴ $\bold{X_C}$ = ωC
$\bold{X_L}$ = 1/ωL
1/ωL = ωC
ω² = $\bold{\frac{1}{LC}}$
So , ω = $\bold{\frac{1}{\sqrt{LC}}}$
Hence, resonant frequency = $\bold{\frac{1}{2\pi\sqrt{LC}}}$
Now, put L = 8H and C = 0.5μF = 5 × 10⁻⁶ F
then, f = 79.57 Hz