Use the step-by-step method below to solve this problem Problem Step-by-step met

Question

Use the step-by-step method below to solve this problem

Problem

Step-by-step method to follow:

For the circuit to the right follow the step-by-step procedure to find the complex amplitude of as a function of angular frequency In addition we are asked to find the quantities derived from the complex amplitude: real amplitude, imaginary amplitude, magnitude, and phase, as functions of angular frequency. The voltage Divider revisited. The circuit to the right can be though of as a voltage divider which is dependent on frequency. We are asked to find the complex of as a function of angular frequency In complex amplitude: real amplitude, imaginary amplitude, magnitude, and phase as functions of angular frequency. First find the complex amplitude of The complex amplitude is Lets look at our results, We are particularly interested in the magnitude. The denominator is .At low frequencies where the magnitude is nearly unity. At high frequency where term dominates so that thus the magnitude drops off like in this region. The transition between the two regions occurs at the point where hence We can solve for the frequency of this point and obtain the following important result. I have labeled this frequency with the subscript C because it is often called the corner frequency. Sometimes you will see the equation of the magnitude written in this form: In these calculations remember that times ohm = second. You will also need to use the context of the equation to distinguish between and because formally they both have units of second so be careful!

Explanation / Answer

sol)

1)let the impdance of capcitor = Z1 = 1/jwC

and the impedance of resistor = Z2 = R

by using voltage division rule

we can find

step 1)

V0= Vin*Z2/(Z1+Z2)

substituting Z1 and Z2

V0/Vin = R /(1/jwC+R) = jwRC/(1+jwRC)

step 2) magnitude = sqrt(real^2+img^2)/sqrt(real^2+img^2)

= sqrt(0^2+jwRC^2)/sqrt(1^2+jRC^2)

|Vout/Vin |= wRC/sqrt(1+(wRC)^2))

arg (vout/vin) = tan inverse (wrc/0) - tan inverse(wRC/1)

= 90 - tan invers (wRC)

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