Problem 15.116 Challenge

กำหนดให้ \(ΔV = 10.0 V, R = 50.0 Ω, L = 0.300 H\) และ \(C = 1.00 μF\)

a) จาก \(X_{L}= 3X_{C}\)

\(\omega L =\frac{3}{\omega C}\)

\(\omega ^{2} =\frac{3}{LC}\)

\((2\pi f)^{2} =\frac{3}{LC}\)

\(f =\frac{1}{2\pi}\sqrt{\frac{3}{LC}}= 503 Hz \;\blacksquare\)

b)

\(_{\Delta VL= \omega LI = 2\pi f\omega LI = 948I}\)

\(_{\Delta V = 10.0 V}\)

\(\frac{_{φ}}{_{I}}_{\Delta VR= RI = 50I}\)

\(_{\omega = 2\pi f = 3,160 Hz}\)

\(_{\Delta VC=}\frac{_{I}}{_{\omega C}}_{=}\frac{_{I}}{_{2\pi fC}}_{= 316I}\)

\(\;\blacksquare\)

c) จาก \(tanφ = \frac{X_{L}-X_{C}}{R}\)

\(φ = \tan ^{-1}(\frac{X_{L}-X_{C}}{R})\)

\(φ = 85.5° \;\blacksquare\)

d) จาก \(Z = \sqrt{R^{2}+(X_{L}-X_{C})^{2}}= 634 Ω\)

จาก \(ΔV = IZ\)

\(I =\frac{\Delta V}{Z}\)

\(I = 15.8 mA \;\blacksquare\)