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Chapter 23: Q82PE (page 863)

At what frequency will an\(80.0\,{\rm{mF}}\)capacitor have a reactance of\(0.250\,{\rm{\Omega }}\)?

Short Answer

Expert verified

The frequency at which the capacitor have a reactance is obtained as, \(7.96\,{\rm{Hz}}\).

Step by step solution

01

Identification of the given data

The given data can be listed below as,

  • The capacitor resistance is,\({X_C} = 0.250\,{\rm{\Omega }}\).
  • The frequency is, \(C = 80.0\,{\rm{mF}}\).
02

Definition of frequency

Frequency is the measure of the number of cycles or periods per second. The hertz is the SI unit for frequency (Hz). One cycle per second equals one hertz.

03

Evaluating the inductive resistance

The inductive reactance is evaluated using the formula:

\({X_C} = \frac{1}{{2\pi fC}}\)

Solving for the frequency as:

\(f = \frac{1}{{2\pi {X_C}C}}\)

Substitute all the value in the above equation.

\(\begin{aligned} f &= \frac{1}{{2\pi \times 0.250\,{\rm{\Omega }} \times 0.08\,{\rm{F}}}}\\ &= 7.96\,{\rm{Hz}}\end{aligned}\)

Therefore, the capacitance used to produce a reactance is obtained as, \(7.96\,{\rm{Hz}}\).

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