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January 29, 2015

January 29, 2015

Posted by **Sandhya** on Saturday, March 29, 2008 at 6:37am.

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

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**Sandhya**, Saturday, March 29, 2008 at 6:40am(d) take Vin = 5 volts coswt

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**drwls**, Saturday, March 29, 2008 at 6:47amIf this was a multiple choice answer, what was the question?

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**Sandhya**, Saturday, March 29, 2008 at 7:38amIn 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.

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**drwls**, Saturday, March 29, 2008 at 9:38am(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.

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**drwls**, Saturday, March 29, 2008 at 9:44amFor assistance with the calculation, and a review of the subject, see

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.html

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**Sandhya**, Saturday, March 29, 2008 at 10:49amThanks. But I want impedance & voltage gain in polar form as modZ*expiwt

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**drwls**, Saturday, March 29, 2008 at 12:37pmThe 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.

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**Sandhya**, Saturday, March 29, 2008 at 2:12pmThank u very much

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