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Chapter 30: Problem 33

At what frequency will a \(10.0-\mu \mathrm{F}\) capacitor have reactance \(X_{C}=200 . \Omega ?\)

Short Answer

Expert verified
Answer: The frequency at which the 10.0 µF capacitor will have a reactance of 200 Ω is approximately 7957.75 Hz.

Step by step solution

01

Write down the given values and formula

We are given the values for capacitive reactance (X_C) and capacitance (C). Write down these values: Capacitive Reactance, \(X_{C} = 200 \Omega\) Capacitance, \(C = 10.0 \times 10^{-6} \mathrm{F}\) We will use the formula for capacitive reactance to solve for the frequency (f): \(X_{C} = \frac{1}{2 \pi f C}\)
02

Solve the equation for frequency (f)

Rearrange the formula to solve for frequency (f): \(f = \frac{1}{2 \pi X_{C} C}\)
03

Substitute the given values and calculate frequency (f)

Plug in the given values of X_C and C into the equation: \(f = \frac{1}{2 \pi (200 \Omega)(10.0 \times 10^{-6} \mathrm{F})}\) Now, calculate the frequency (f): \(f \approx 7957.75 \mathrm{Hz}\)
04

Write the final answer

The frequency at which the \(10.0-\mu \mathrm{F}\) capacitor will have a reactance of \(200 . \Omega\) is approximately \(7957.75 \mathrm{Hz}\).

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