A series LC circuit has capacitance 50 and inductance of 500. Calculate the frequency at which the circuit will resonate.(take pie as 3.142)?
F = 1/2pi(sqrtLC).
C = 50uF?
L = 500uh?
To calculate the resonant frequency of a series LC circuit, you can use the formula:
\( \text{Resonant frequency} = \frac{1}{2\pi \sqrt{LC}} \)
Given:
Capacitance (C) = 50
Inductance (L) = 500
Value of π (π) = 3.142
Substituting the given values into the formula, we get:
\( \text{Resonant frequency} = \frac{1}{2 \times 3.142 \times \sqrt{50 \times 500}} \)
Simplifying:
\( \text{Resonant frequency} = \frac{1}{2 \times 3.142 \times \sqrt{25000}} \)
Taking the square root of 25000:
\( \text{Resonant frequency} = \frac{1}{2 \times 3.142 \times 158.114} \)
Multiplying and simplifying further:
\( \text{Resonant frequency} = \frac{1}{990.782} \)
Taking the reciprocal:
\( \text{Resonant frequency} = 0.001009 \)
So, the resonant frequency of the series LC circuit is approximately 0.001009 Hz.