Please show work so that I can figure out how to do this problem correctly~ Than
ID: 1270737 • Letter: P
Question
Please show work so that I can figure out how to do this problem correctly~ Thanks
e.)If R=200 Ohms, L=0.40H, C=6.0MicroFarad, V=30V and omega =200 rad/s what are the readings of the five voltmeters V1,.....V5? (Please show work)
Five infinite impedance voltmeters which read rms values V1,...,V5 are connected as shown. The voltage source has constant amplitude V and adjustable angular frequency omega. An alternating current with amplitude I flows through the main body of the circuit. The resistor has resistance R, the inductor has inductance L, and the capacitor has capacitance C. Show that the current amplitude (as a function of omega)is I = V / R2+(omega L-1/omega C)2 At what value of omega is the rms value V1 at a maximum? At what value of omega is the rms value V2 at a maximum?Explanation / Answer
a)
Ipk = Vpk/Z
Where: Z, is the total impedance of the circuit
Z = SQRT [R^2 + (XL-XC)^2]
Where: XL and XC is the inductive and capacitive reactances respectively
XL = 2 x pi x f x L and XC = 1/(2 x pi x f x C)
But, omega = 2 x pi x f; therefore
XL = omega x L and XC = 1/omega C)
Z = SQRT [R^2 + ((omega x L) - 1/(omega x C))^2]
Ipk = Vpk/SQRT [R^2 + ((omega x L) - 1/(omega x C))^2]
b)
Maximum V1rms occurs when Irms for the series circuit is maximum
This maximum current occurs at resonance when the XL-XC of Z = SQRT [R^2 + (XL-XC)^2] becomes zero.
In such a case the impedance of the circuit is simply R and V1rms = V/(sqrt [2] x R)
omega x L = 1/omega x C
omega^2 = 1/LC
omega - 1/SQRT [LC]
c)
V2 rms is maximum when the inductive reactance XL>>R this occurs when omega approaches infinity
d)
V3 rms is maximum when the capacitive reactance, XC>>R and this occurs when omega = zero
equ to the frequency = zero or DC.
e) was already answered above, and is correct