Answered: A 41.1 Q resistor, a 64.5 µF capacitor…

A 41.1 Q resistor, a 64.5 µF capacitor and a 8.27 mH resistanceless coil are in series with an AC source (Vrms = 213 V, ƒ = 89.4 Hz). Find the rms current, in A, in this circuit.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter33: Inductors And Ac Circuits

Section: Chapter Questions

Problem 31PQ

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Question in the attachment

A 41.1 Q resistor, a 64.5 µF capacitor and a 8.27 mH resistanceless coil are in series with an AC source (Vrms = 213 V, f = 89.4 Hz). Find the rms current, in A, in this
circuit.

Expert Solution

Step 1

$V_{r m s} = 213 V f = 89.4 H z R = 41.1 o h m X_{c} = 1 / w c X_{c} = 1 / (2 π * 89.4 * 64.5 * 10^{- 6}) X_{c} = 27.6 ohm X_{L} = w L X_{L} = 2 π * 89.4 * 0.00827 X_{L} = 4.645 ohm$

Impedence (Z) :

$Z = \sqrt{R^{2} + (X}$ _c- X_L)2Z = (41.1)2 +(27.6-4.645)2Z = 47.075 ohm

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