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Concept

Problem: A capacitance C and an inductance L are operated at the same angular frequency. Part AAt what angular frequency will they have the same reactance?Part B If L = 5.50 mH and C = 3.70 mu F, what is the numerical value of the angular frequency in part A?Part CWhat is the reactance of each element?

FREE Expert Solution

The reactance of an inductor:

$\overline{){{\mathbf{X}}}_{{\mathbf{L}}}{\mathbf{=}}{\mathbf{\omega }}{\mathbf{L}}}$

The reactance of a capacitor:

$\overline{){{\mathbf{X}}}_{{\mathbf{C}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{\omega }\mathbf{C}}}$

(A)

XL = XC

ωL = 1/ωC

ω2LC = 1

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Problem Details

A capacitance C and an inductance L are operated at the same angular frequency.

Part A

At what angular frequency will they have the same reactance?

Part B

If L = 5.50 mH and C = 3.70 mu F, what is the numerical value of the angular frequency in part A?

Part C

What is the reactance of each element?