A sinusoidal voltage v = 45.0 sin 100 t , where v is in volts and t is in second
ID: 2029842 • Letter: A
Question
A sinusoidal voltage v = 45.0 sin 100t, where v is in volts and t is in seconds, is applied to a series RLC circuit with L = 155 mH, C = 99.0 µF, and R = 72.0 .
(a) What is the impedance of the circuit?
A sinasodal veltage , 45 .O sn 100, where Sris in vots and t is 'n seconds.s appliad to series RLC crcuit with 1-155 mH, C-99.0 se·and R , 72 0e. (a what s the impedance or the circut [c) Detemre the nunarical valae forde in the equation-mal sin (art-4). dDeermine the numerical value for inthe equetion-a Sn (ut-Explanation / Answer
a)
impedence is z = sqrt(R^2+(XL-Xc)^2)
R = 72 ohm
XL = w*L = 100*155*10^-3 = 15.5 ohm
Xc = 1/(w*C) = 1/(100*99*10^-6) = 101 ohm
then
z = sqrt(72^2+(15.5-101)^2) = 111.77 ohm
b) maximum current is imax = 45/111.7 =0.402 A
c) w = 100 rad/s
d) phi = tan^(-1)((XL-Xc)/R)
phi = tan^(-1)((15.5-101)/72)
phi = -49.9 deg