# Question about Resonance in LCR circuits

Joined May 7, 2007
2
Hello everybody ..

I have this question in my assignment and I really can't understand it

May anyone of you help plz ?

Draw a graph which shows how the phase difference, ( Phi ) , between the current, ( I total ) , flowing through a series LCR circuits and the total voltage, ( V total ) , across it varies with the angular frequency , ( Omega) of the applied voltage. Use component values of L= 0.01H, C=10 micro Faradand R= 10 Ohm and a frequency range = 0-10000 in your calculations.

Comment braifly on your results , using phasor diagram to explain your observations.

What happens to the shape of the graph if the value of R is increased to 100 Ohm.

Thanks #### recca02

Joined Apr 2, 2007
1,214
try solving the circuit first using simple kvl and expressing voltage,current ,reactances in polar form.
find out total current in crkt the phase difference between voltage and current quantities will be the angle difference between them.
depending on the value of the angle +ve or -ve the current will lead or lag the voltage by that angle.
you may also want to find voltages across cap and ind by multiplying individual reactances with the current in ckt.
now construct a vector(phasor) dia showing the vectors of voltages across each comp with respect to applied voltage.also plot current vector relative to it.

by graph do they mean sinusoidal representation of quantities.
in that case draw sine waves of current and voltage using same scale and
depending on the leading or lagging angle the voltage will arrive at
value earlier or later the current (like zero or maxima) by that angle.

i m not sure what they mean by using the range of frequencies take any arbitrary value of frequency between those two values.

edit: in phasor dia the direction of the quantities is defined by their respective angle obtained by calculations in polar form.
these angles are relative to the reference quantity (here supply voltage)
scale for current and voltage may be taken different but for voltage and voltage drops they must remain same.

Joined May 7, 2007
2

#### recca02

Joined Apr 2, 2007
1,214
feel free to ask if you have any doubt.

edit:sorry i didnt read the question properly last time.

it is clear that the phase difference between the voltage and the current is going to change from leading to lagging with
change in frequency ; may be u shud solve for current taking omega(w) as variable.
establish a relation between current and w and check phase angle for different frequency.
based on which u have to draw a plot of phase versus frequency.
from plot it wud be clear that current and voltage are in phase when resonance occurs and for higher or lower frequency the current leads or lags.

check the case again with value of resistor changed.