For a L-C-R circuit Vin = v0*expjwt. Vout is taken across R

Question

a) Calculate the impedance of the circuit measured from the input side. Express the impedance in polar form.
b) Calculate the gain=Vout/Vin and express the ratio in polar form.
c) Sketch the amplitude and phase of the gain as a function of the angular frequency of the input voltage.
d) For an input voltage where the angular frequency is 2pi x 5 kHz, and L= 20 mH, C==0.01 *mu* F, and R= 3 k ohm, Sketch the wave form of input and output voltage as a function of time. The relative phase of the output and input must be clearly marked in the drawings

Answer 1

(d) take Vin = 5 volts coswt

Answer 2

If this was a multiple choice answer, what was the question?

Answer 3

In a series L-C-R circuit Vin = V0*expjwt.Vout is taken across R.
(a)Calculate the impedance of the circuit measured from the input side.Express the impedance in polar form.
(b)Calculate Vout/Vin and express the ratio in polar form
(c)Sketch the amplitude and phase of the gain as a function ofangular frequency of the input voltage
(d)For an input voltage V = 5 volts coswt where the angular frequency is 2pi*5kHz ,L = 20mH,C = 0.01*mu*F and R = 3k ohm sketch the wave forms of the i/p & o/p voltages as a function of time.

Answer 4

(a) Add the impedances of the three circuit elements. They are R, iwL and -i/wC, where I is sqrt (-1). Your L is 20*10^-3 H and the C is 10^-8 F if your stated units are milliHenries and microfarads. Call the total impedance Zt, and compute its value.

(b) Vout = I*R = (Vin/Zt)*R
Vout/Vin = R/Zt

(c and d) We can't draw graphs for you. There will be a frequency when the gain |Vout/Vin| is a maximum. It will be the value of w for which wL = 1/(wC). This is the resonant frequency of the cricuit.

Answer 5

For assistance with the calculation, and a review of the subject, see
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.html

Answer 6

Thanks. But I want impedance & voltage gain in polar form as modZ*expiwt

Answer 7

The magnitude or "mod" is the square root of the sum of the squares of real and imaginary terms. The phase angle in the arctangent of the ratio (imaginary part/real part). Most of this was explained in the link that I gave you earlier.

BobPursley is more experienced with AC electronics; perhaps he will be able to provide further assistance.

Answer 8

Thank u very much