Question

A 8500-pF capacitor is connected in series to a 33.0-μH coil of resistance 4.90 Ω. a) What is the total impedance of the circuit? b) What is the resonant frequency of the circuit?

Answer 1

The total impedance of a series RLC circuit is found using the formula for Z which considers R, X_L, and X_C. The resonant frequency is calculated with the formula f_0 = 1 / (2π√(LC)), and the impedance at the resonant frequency equals the resistance, as the reactances cancel each other out.

Step-by-step explanation:

The total impedance Z of a series RLC circuit (with resistance R, inductance L, and capacitance C) can be calculated using the formula:

Z = √(R^2 + (X_L - X_C)^2)

Where X_L is the inductive reactance (X_L = 2πfL) and X_C is the capacitive reactance (X_C = 1/(2πfC)). To find the resonant frequency f_0 for an RLC circuit, the following formula can be used:

f_0 = 1 / (2π√(LC))

Using the given values, L = 33.0 μH and C = 8500 pF, we can calculate the resonant frequency and then the impedance at that frequency which will only be affected by the resistance since X_L will equal X_C at resonance.