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Chapter 28: Problem 39

Show that the unit of both capacitive and inductive reactance is the ohm.

Short Answer

Expert verified
Yes, both capacitive reactance and inductive reactance are measured in ohms (\(\Omega\)).

Step by step solution

01

Determine the units for capacitive reactance

Starting with the formula for capacitive reactance \(X_C = 1/2\pi fC\). We know that the frequency \(f\) is measured in Hertz (\(Hz\)), capacitance \(C\) is measured in Farads (\(F\)) and the reactance \(X_C\) is what we want to compute. Multiplying Hertz by Farads gives \(Hz \cdot F = s^{-1}\cdot C^{-1}\). Therefore, in this equation, all units except ohms cancel out, confirming that the unit of capacitive reactance \(X_C\) is, indeed, ohms (\(\Omega\)).
02

Determine the units for inductive reactance

Moving on to the formula for inductive reactance \(X_L = 2\pi fL\). Frequency \(f\) is again measured in Hertz (\(Hz\)), and inductance \(L\) is measured in Henrys (\(H\)). When Hertz is multiplied by Henrys, \(Hz \cdot H = s^{-1}\cdot H\), which simplifies to Ohms (\(\Omega\)), confirming that the unit of inductive reactance \(X_L\) is, as suspected, ohms (\(\Omega\)).

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Most popular questions from this chapter

A series \(R L C\) circuit with \(R=1.3 \Omega, L=27 \mathrm{mH},\) and \(C=0.33 \mu \mathrm{F}\) is connected across a sine-wave generator. If the capacitor's peak voltage rating is \(600 \mathrm{V},\) what's the maximum safe value for the generator's peak output voltage when it's tuned to resonance?

Find the resonant frequency of an \(L C\) circuit consisting of a 0.22 -\muF capacitor and a 1.7 -mH inductor.

Why is Equation 28.5 not a full description of the relation between voltage and current in a capacitor?

An LC circuit with a 20 - \(\mu\) F capacitor oscillates with period \(5.0 \mathrm{ms}\). The peak current is 25 mA. Find (a) the inductance and (b) the peak voltage.

You're Chief Financial Officer for a power company, and you consult your engineering department in an effort to minimize powerline losses. Your power plant produces \(60-\mathrm{Hz}\) power at \(365 \mathrm{kV}\) rms and \(200 \mathrm{A}\) rms, and delivers it via transmission lines with total resistance \(100 \Omega .\) You ask the engineers for the percentage of power that's lost. They reply that it depends on the power factor. What's the percentage loss for power factors of (a) 1.0 and (b) \(0.60 ?\)
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