Question

What is the resonant frequency (in hz) of a resistor, capacitor, and inductor connected in series if R= 200 Ω, L= 2.2 H, and C= 5.8 μF?

Answer 1

The resonant frequency of an RLC series circuit with the given parameters is approximately 14.01 Hz, calculated using the formula f = 1 / (2π√(LC)).

Step-by-step explanation:

The question asks to calculate the resonant frequency of a series RLC circuit given the values of resistance (R), inductance (L), and capacitance (C). The resonant frequency for an RLC circuit can be found using the formula:

f = 1 / (2π√(LC))

where:

• f is the resonant frequency in hertz (Hz)
• L is the inductance in henries (H)
• C is the capacitance in farads (F)

We are given that R = 200 Ω, L = 2.2 H, and C = 5.8 μF (which is 5.8 x 10-6 F when converted to farads). Inserting these values into the formula, we get:

f = 1 / (2π√(2.2 H x 5.8 x 10-6 F))

Calculating this we find:

f ≈ 1 / (2π√(0.01276))

f ≈ 1 / (0.0714)

f ≈ 14.01 Hz

Therefore, the resonant frequency of the circuit is approximately 14.01 Hz.