Physics
posted by Sandhya .
For a LCR 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 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

(d) take Vin = 5 volts coswt

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

In a series LCR 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. 
(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. 
For assistance with the calculation, and a review of the subject, see
http://hyperphysics.phyastr.gsu.edu/hbase/electric/serres.html 
Thanks. But I want impedance & voltage gain in polar form as modZ*expiwt

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. 
Thank u very much