Question

You have a 205 Ω resistor, a 0.396 h inductor, a 5.02 μf capacitor, and a variable-frequency ac source with an amplitude of 2.90 v. You connect all four elements together to form a series circuit. What is the total impedance of the circuit?

Answer 1

The total impedance (Zₜₒₜₐₗ) of the circuit is approximately 205 + j(2.90 × 0.396 - 1 / (2.90 × 5.02)) Ω.

Step-by-step explanation:

In a series circuit with a resistor, inductor, capacitor, and AC source, the total impedance (Zₜₒₜₐₗ) is the sum of the resistance (R) and the reactance due to the inductor (L) and capacitor (C). The formula for Zₜₒₜₐₗ is R + j(ωL - 1 / (ωC)), where j is the imaginary unit and ω is the angular frequency.

For this circuit, the given values are R = 205 Ω, L = 0.396 h, C = 5.02 μF, and the AC source has an amplitude of 2.90 V. The angular frequency (ω) can be calculated as 2πf, where f is the frequency of the AC source.

Substituting these values into the formula, we get the expression for Zₜₒₜₐₗ. The real part (205 Ω) represents the resistance, while the imaginary part accounts for the phase shifts introduced by the inductor and capacitor. The final result is a complex impedance that characterizes the circuit's opposition to the alternating current.