# L-C-R circuit solution

#### friendforall123

Joined Oct 18, 2005
4
I have circuit with a voltage source having equation E = 20*sin(15*t).
It has two resistances (R1, R2), one capacitor © and one inductor (L).
C is in parallel with R2 and L (which are both in series).
the above ciruit is in series with R1.

this gives us two governing equations:
E = I1*R1 + (1/C) * ∫ (I1-I2) dt

and

I2*R2 + L (dI2 / dt) + (1/C) * ∫ (I1-I2) dt = 0

initial values of I1 and I2 are zeros. I need to find the value of I1 and I2 at corresponding time = 1, 2, 3 .... 10 secs and then draw the plot till 100 secs.
Can somebody help me in finding the solution to this question. or maybe if someone can guide me if this can be done in MATLAB and how....I will be really greatful thanks a lot

#### hgmjr

Joined Jan 28, 2005
9,029
Were you provided component values for R1, R2, C, and L as part of the problem?

hgmjr

#### friendforall123

Joined Oct 18, 2005
4
yes, R1= 100, R2 = 50, C = 0.001, and L = 2

Originally posted by hgmjr@Oct 18 2005, 04:19 PM
Were you provided component values for R1, R2, C, and L as part of the problem?

hgmjr
[post=11094]Quoted post[/post]​

#### hgmjr

Joined Jan 28, 2005
9,029
Hi Friendforall123,

After thinking about the best way to analyze your circuit I believe the easiest way to get to the answers you seek is by using vector analysis.

There is a very good Vector Analysis Tutorial located on this website. I recommend that you take a look at the material and then take a shot at applying it to your circuit.

One of the first things you will need to do is determine the capacitive reactance and the inductive reactance in your circuit. HINT: You can find the value of ω from the expression for the source voltage.

Next, You will need to find the total impedance of your circuit.

For example, I performed the analysis and for the current (I2) flowing just in the branch containing the series combination of R2 and L and came up with the following value.

I2 = 0.1347/-45.00 amps (polar notation) (Updated my figures)

or in complex number notation

I2 = 0.0952 - j0.0952

-------------------------- Edited on 10/24/05 --------------

The value of I2 given above is true for all values of E = 20*sin(15t) in which t = (2*pi*n)/15 where n is a member of the set of positive integers greater than or equal to 2.

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Once you have found both I1 and I2 you will be able to write the expression that will allow you to calculate the value of each at the time points you mentioned in your posting. Also with the same expressions you can put them into an EXCEL spreadsheet and plot the values all the way out to 100 seconds.

If you will post your answers, I will compare them to mine.

Good Luck,
hgmjr