Question

In an RLC series circuit with a 2.50 Ω resistor, 100 μH inductor, and 80.0 μF capacitor, find the circuit’s impedance at 120 Hz.

a) 4.52 Ω
b) 2.50 Ω
c) 4.65 Ω
d) 3.18 Ω

Answer 1

The impedance of the RLC series circuit at 120 Hz is approximately 4.52 Ω.

Step-by-step explanation:

The impedance (Z) of an RLC series circuit is given by the formula:

Z = sqrt((R^2) + ((XL - XC)^2))

Where:

• R is the resistance
• XL is the inductive reactance, given by 2 * pi * frequency * inductance
• XC is the capacitive reactance, given by 1 / (2 * pi * frequency * capacitance)

Plugging in the given values:

Z = sqrt((2.50^2) + ((2 * pi * 120 * 100 x 10^-6) - (1 / (2 * pi * 120 * 80 x 10^-6)))^2)

Z ≈ 4.52 Ω