Calculate capacitive reactance, inductive reactance, and resonance frequency given specific circuit…

Question

Calculate capacitive reactance, inductive reactance, and resonance frequency given specific circuit parameters.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

1) Capacitive Reactance

Identify the given values and the formula for capacitive reactance.
Given: Capacitance $C = 10 \text{ mF} = 10 \times 10^{-3} \text{ F}$ , Frequency $f = 60 \text{ Hz}$ .
The formula for capacitive reactance ( $X_C$ ) is:
$X_C = \frac{1}{2\pi f C}$
Substitute the values and calculate $X_C$ .
$X_C = \frac{1}{2\pi (60 \text{ Hz}) (10 \times 10^{-3} \text{ F})}$ $X_C = \frac{1}{1.2\pi} \Omega$ $X_C \approx \frac{1}{3.7699} \Omega$ $X_C \approx \boxed{0.265 \Omega}$
2) Inductive Reactance
Identify the given values and the formula for inductive reactance.
Given: Inductance $L = 2 \text{ H}$ , Frequency $f = 60 \text{ Hz}$ .
The formula for inductive reactance ( $X_L$ ) is:
$X_L = 2\pi f L$
Substitute the values and calculate $X_L$ .
$X_L = 2\pi (60 \text{ Hz}) (2 \text{ H})$ $X_L = 240\pi \Omega$ $X_L \approx \boxed{753.98 \Omega}$
3) Resonance Frequency
Identify the given values and the formula for resonance frequency.
Given: Inductance $L = 200 mH = 200 \times

Calculate capacitive reactance, inductive reactance, and resonance frequency given specific circuit parameters.