For a 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 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 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.
(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.phy-astr.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
To answer your questions, we first need to understand the properties of a L-C-R circuit.
In a L-C-R circuit, there are three components - Inductor (L), Capacitor (C), and Resistor (R). The input voltage is given as Vin = v0 * exp(jwt), where v0 is the amplitude, w is the angular frequency, and t is time. The output voltage is taken across the resistor R, which is denoted as Vout.
a) To calculate the impedance of the circuit measured from the input side, we need to calculate the impedance for each component separately and then add them up.
1. The impedance of an inductor can be calculated using the formula Zl = jwL, where j is the imaginary unit, w is the angular frequency, and L is the inductance. In polar form, Zl can be expressed as Zl = |Zl| * exp(jθl), where |Zl| is the magnitude of impedance and θl is the phase angle.
2. The impedance of a capacitor can be calculated using the formula Zc = 1 / (jwC). In polar form, Zc can be expressed as Zc = |Zc| * exp(jθc), where |Zc| is the magnitude of impedance and θc is the phase angle.
3. The impedance of a resistor is simply its resistance value, R.
To find the total impedance, Z, we add the impedances of all three components in series. So, Z = Zl + Zc + R.
b) The gain of the circuit can be calculated as the ratio of Vout to Vin. In polar form, the gain can be expressed as gain = |gain| * exp(jθg), where |gain| is the magnitude of gain and θg is the phase angle.
To find the gain, we divide the magnitude of Vout by the magnitude of Vin, and subtract the phase angle of Vin from the phase angle of Vout.
c) To sketch the amplitude and phase of the gain as a function of the angular frequency of the input voltage, we can vary the angular frequency and calculate the gain for different frequency values. Plotting the magnitude and phase angle of the gain against the angular frequency will give us the desired graph.
d) To sketch the waveform of the input and output voltage as a function of time, we can use the given values of angular frequency (2pi x 5 kHz), inductance (L = 20 mH), capacitance (C = 0.01 *mu* F), and resistance (R = 3 k ohm) to calculate the values of Vin and Vout at different time intervals. Plotting the values on a graph will give us the waveform. The relative phase of the output and input can be marked on the graph to indicate the phase difference.
In summary, to answer your questions about the L-C-R circuit, we need to calculate the impedance, gain, and waveform using the relevant formulas and given values.