If the voltage in the circuit is maintained by an AC source operating at f = 60.0 Hz and the resonant frequency of the circuit is f0 = 90.0 Hz, what are the values of C (in µF) and L (in mH) in the circuit?
Question
If the voltage in the circuit is maintained by an AC source operating at f = 60.0 Hz and the resonant frequency of the circuit is f0 = 90.0 Hz, what are the values of C (in µF) and L (in mH) in the circuit?
Solution
The resonant frequency of a circuit is given by the formula:
f0 = 1 / (2π√(LC))
where: f0 is the resonant frequency, L is the inductance, and C is the capacitance.
We can rearrange this formula to solve for L and C.
Given that f0 = 90.0 Hz, we can solve for L as follows:
L = 1 / (4π²f0²C)
And for C as follows:
C = 1 / (4π²f0²L)
However, without additional information, we cannot determine the specific values of L and C. We need either the value of L to find C, or the value of C to find L.
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