782016 1155 PM 9 Time Remaining 56 M 52 S Gradebook Question

7/8/2016 11:55 PM 9 Time Remaining: 56 M 52 S Gradebook Question 6 of 6 Sapling Learning Map this question was written by Sean Condry at Walters State Community College A voltage is applied to the \"RLC circuit shown. The values for the components are given below, and the voltage supplied to the circuit is this: v-90.0sin(251-7.6) 185 3.55 F 44.3 mH Yo Oe Answer the three questions below, using three signifcant figures Part A What is the \"rms\" value of the applied voltage? Number rms Part B: If the frequency of the applied voltage is increased, what happens to the value of. the inductive reactance? the capactive reactance? O It increases the resistance? O It increases. O It increases. Previous NextSave And Exit Previous Next save And Exit-

Solution

(A) Vrms = Vmax / sqrt(2)

      = 90 / sqrt(2) = 63.64 volt

(B) R is independent of frequency. so resistance will remain same.

XL = 2 pi f L

if frquency is increased then inductive reactance will also increase/

Xc = 1/(2 pi f C)

capacitive reactance will decrease.

(C) at resonance frequency:

wL = 1/wC

w0 = 1 / sqrt(LC)

w0 = 1 / sqrt(44.3 x 10^-3 x 3.55 x 10^-6)

w0 = 2521.65 rad/s

in Hz

w0 = 2521.65 / 2pi = 401.33 Hz