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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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Most popular questions from this chapter

A large research solenoid has a self-inductance of 25.0 H (a) What induced emf opposes shutting it off when 100 Aof current through it is switched off in 80.0ms? (b) How much energy is stored in the inductor at full current? (c) At what rate in watts must energy be dissipated to switch the current off in 80.0ms? (d) In view of the answer to the last part, is it surprising that shutting it down this quickly is difficult?

A \(500\)-turn coil with a\(0.250{\rm{ }}{m^2}\)area is spun in the Earth’s \(5.00 \times {10^{ - 5}}{\rm{ }}T\) field, producing a \(12.0{\rm{ }}kV\) maximum emf.

(a) At what angular velocity must the coil be spun?

(b) What is unreasonable about this result?

(c) Which assumption or premise is responsible?

A plug-in transformer, like that in Figure\(23.29\), supplies\(9.00{\rm{ }}V\)to a video game system.

(a) How many turns are in its secondary coil, if its input voltage is\(120{\rm{ }}V\)and the primary coil has\(400\)turns?

(b) What is its input current when its output is\(1.30{\rm{ }}A\)?

What is the peak emf generated by rotating a 1000-turn, \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{ T}}\) diameter coil in the Earth’s magnetic field, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in \({\rm{10}}{\rm{.0 ms}}\)?

High-frequency noise in AC power can damage computers. Does the plug-in unit designed to prevent this damage use a large inductance or a large capacitance (in series with the computer) to filter out such high frequencies? Explain.
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