Question

A 68 Ω resistor, an 8.6 μF capacitor, and a 36 mH inductor are connected in series in an ac circuit.

Part A: Calculate the impedance for a source frequency of 300 Hz.

Part B: Calculate the impedance for a source frequency of 30.0 kHz.

Express your answers to two significant figures and include the appropriate units.

Answer 1

A)

f = frequency = 300 Hz

R = resistance of the resistor = 68 Ω

C = Capacitance of the capacitor = 8.6 x 10^-6 F

L = Inductance of indutor = 36 mH = 0.036 H

X_c = Capacitive reactance = 1/(2fC) = 1/(2(3.14)(300)(8.6 x 10^-6)) = 61.72 Ω

X_L = inductive reactance = 2fL = 2(3.14)(300)(0.036) = 67.824 Ω

Impedance is given as

z = sqrt(R² + (X_L - X_c)²)

z = sqrt((68)² + (67.824 - 61.72)²)

z = 68 Ω

Part B)

f = frequency = 30000 Hz

R = resistance of the resistor = 68 Ω

C = Capacitance of the capacitor = 8.6 x 10^-6 F

L = Inductance of indutor = 36 mH = 0.036 H

X_c = Capacitive reactance = 1/(2fC) = 1/(2(3.14)(30000)(8.6 x 10^-6)) = 0.62 Ω

X_L = inductive reactance = 2fL = 2(3.14)(300)(0.036) = 6782.4 Ω

Impedance is given as

z = sqrt(R² + (X_L - X_c)²)

z = sqrt((68)² + (6782.4 - 0.62)²)

z = 6782.12 Ω

z = 6.8 x 10³ Ω