Frequency of AC power
The above is an RLC series circuit, where the resistance of the resistor, the self-inductance of the inductor and the capacitance of the capacitor are
,
and
, respectively. If the impedance of the circuit is
, then what is the frequency of the AC power supply?
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(Impedence (Z) is calculated by Z = [R²+(Xc-Xl)²]½
Where Xc = 1/ωC and Xl = ωL ...............①
Where Xc denotes capacitive reactance and Xl denotes inductive reactance and R denotes resistance)
Given that the Impedence (Z) = R, shows that the circuit is in resonance condition, and in this condition,
Xl = Xc
ωL = 1/ωC from ①
Which gives
ω² = 1/LC
Or
ω = 1/(LC)½
Now, substituting ω = 2πf
We get f = 1/2π (LC)½