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Chapter 28: Problem 40

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

Short Answer

Expert verified
Therefore, it is proven that both inductive reactance and capacitive reactance are measured in ohms.

Step by step solution

01

Inductive Reactance

Inductive reactance \(X_L\) is given by the formula \(X_L = 2\pi fL\), where \(f\) is the frequency in hertz and \(L\) is the inductance in henry. So, the unit of \(X_L\) is the product of the units of \(f\) and \(L\), which gives \(Hz \cdot H = s^{-1} . H = s^{-1} . \Omega . s = \Omega\). Hence, the unit of inductive reactance is ohms.
02

Capacitive Reactance

Capacitive reactance \(X_C\) is given by the formula \(X_C = 1/(2\pi fC)\), where \(f\) is the frequency in hertz and \(C\) is the capacitance in farads. So, the unit of \(X_C\) is \(1/ (Hz \cdot F) = s . (C/V) = A^2 . s^3 . N^{-1} . m^{-2} = A^2 . s^3 . kg^{-1} . m^{-3} = A . s . A^{-1} = \Omega\). Hence, the unit of capacitive reactance is ohms.

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Most popular questions from this chapter

Much of Europe uses AC power at \(230 \mathrm{V}\) rms and \(50 \mathrm{Hz}\). Express this AC voltage in the form of Equation \(28.3,\) taking \(\phi_{V}=0\)

A \(40-\) W fluorescent lamp has power factor 0.85 and operates from the \(120-\mathrm{V}\) rms AC power line. How much current does it draw?

A series \(R L C\) circuit has power factor 0.80 and impedance \(100 \Omega\) at \(60 \mathrm{Hz}\). (a) What's the resistance? (b) If the inductance is \(0.10 \mathrm{H},\) what's the resonant frequency?

(a) A \(2.2-\) H inductor is connected across \(120-\mathrm{V}\) rms, \(60-\mathrm{Hz}\) power. Find the rms inductor current. (b) Repeat if the same inductor is connected across the \(230-\mathrm{V}\) rms, \(50-\mathrm{Hz}\) power commonly used in Europe.

The voltage across two components in series is zero. Is it possible that the voltages across the individual components aren't zero? Give an example.
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