Resonant Frequency Calculation in an AC Series Circuit

To calculate the resonant frequency of an AC series circuit, we need to consider the values of resistance (R), inductance (L), and capacitance (C) in the circuit.

Given values:
Resistance (R) = 10Ω
Inductance (L) = 0.2H
Capacitance (C) = 50µF

Step 1: Convert the capacitance to Farads
The given capacitance is in microfarads (µF), so we need to convert it to farads (F) to match the other units in the equation.
1 microfarad (µF) = 1 × 10^(-6) farads (F)
Therefore, 50µF = 50 × 10^(-6) F = 5 × 10^(-5) F.

Step 2: Calculate the angular frequency (ω)
The angular frequency (ω) is calculated using the formula:
ω = 1 / sqrt(LC)
where L is the inductance and C is the capacitance.
Substituting the given values, we get:
ω = 1 / sqrt(0.2 * 5 × 10^(-5))
ω = 1 / sqrt(10^(-6))
ω = 1 / (1 × 10^(-3))
ω = 10^3 rad/s

Step 3: Calculate the resonant frequency (f)
The resonant frequency (f) can be calculated using the formula:
f = ω / (2π)
where ω is the angular frequency.
Substituting the calculated value of ω, we get:
f = 10^3 / (2π)
f ≈ 159.15 Hz

Conclusion:
The resonant frequency of the AC series circuit with a resistance of 10Ω, an inductance of 0.2H, and a capacitance of 50µF is approximately 159.15 Hz. The resonant frequency indicates the frequency at which the circuit resonates, meaning the circuit will have maximum current and minimum impedance at this frequency.

Ok this is done