# Total impedance of a RLC circuit

1. Jan 18, 2012

### andreasoro

Hi, I need to write a c++ program that calculates the total impedance of a simple RLC circuit. I'm given the values of each component (resistance, coil, condenser). The programming part is not a issue however I can't find the formulas for the impedance on the internet. Can someone help me out please? :) thanks a lot

2. Jan 18, 2012

### Curious3141

I wanted to quote the Wiki, but it's been blacked-out. :grumpy:

Anyway...the complex number representations are the neatest representation, and I think C++ can handle complex variables, right?

Capacitance: $Z_C = \frac{1}{j{\omega}C} = \frac{-j}{{\omega}C}$

Inductance: $Z_L = j{\omega}L$

Resistance: $Z_R = R$

For the resistance, the impedance is just the usual resistance. $\omega$ (angular frequency) is equal to $2{\pi}f$, where f is the usual frequency of the alternating current.

Series and parallel arrangements can be treated in the usual fashion, substituting the imaginary/complex reactances and impedances for the usual real resistances.

3. Jan 18, 2012

### andreasoro

Thanks a lot! I don't know if it does, we're supposed to use a struct with two integers representing the real and the imaginary part. Thanks a lot for helping! what is weird is that we're not given ω but just one value for each component (for example "condenser = 4)

4. Jan 18, 2012

### Curious3141

I'm pretty sure (ages ago, when I was programming for fun) that C (not even C++) can handle complex variables. I used it in a fractal generation program I wrote. You have to import the correct library, #include<complex.h> or something of the sort and probably #include<math.h> as well.

5. Jan 18, 2012

### Staff: Mentor

What is the exact phrasing of the problem statement? Is it possible that you're being given the REACTANCES of the L and C components rather than their inductance and capacitance?

6. Jan 18, 2012

### andreasoro

The assignment is in the attachment

#### Attached Files:

• ###### Inf1_exsup_Aufgabe.pdf
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7. Jan 18, 2012

### andreasoro

By the way, I really appreciate it that you're putting so much effort in helping me :)

8. Jan 18, 2012

### andreasoro

Actually I can't even do the programming part, I've been trying all day but I can't figure out how to do it.. I've never programmed before college and our assignment are really hard or at least they seem hard to me... so if you don't have time it's fine :(

9. Jan 18, 2012

### Curious3141

That's a weird assignment. They didn't specify units for any of the values. I assume the resistances are given in ohm, but what about the inductors and capacitors?

They did mention complex numbers, so they clearly want you to manipulate imaginary reactances and complex impedances. But they did not provide any frequency of the voltage source, etc. which is very important in determining the reactances of those components.

This assignment really needs to be clarified. Judging by the dates, unfortunately, it's not a current assignment.

With regard to the programming part, it looks like they want you to build complex arithmetic capabilities into your program, rather than using predefined library functions.

10. Jan 18, 2012

### Curious3141

If I was doing this assignment and I couldn't get clarification, I wouldn't worry too much. I would just assume that those are L and C values in the usual units (H and F, respectively). I would just leave f as a symbolic variable that can be "#define"d should the need arise, and calculate omega based on f.

Then it's just a matter of defining the structure "complex", constructing functions that add, subtract, multiply and divide, then define the series operation as just the sum of two impedances, and the parallel operation as $\frac{Z_1Z_2}{Z_1 + Z_2}$.

11. Jan 18, 2012

### andreasoro

ok thanks a lot for helping! I really appreciate it! The deadline has been changed to friday which means I still have a couple days! I really need to figure it out cuz I still need one point to be admitted to the final exam

12. Jan 18, 2012

### Staff: Mentor

The assignment is poorly written. It is apparent that whoever created the problem didn't fully understand impedance and its dependance on frequency.

I suggest that you add another set of tags, <freq> and </freq>, which allows you to specify the operating frequency of the circuit. This tag set would occur immediately following the <circuit> tag prior to any component specification, and only one per circuit, and would be required for any circuit that contains reactive components (coil or condenser).

With the circuit operating frequency known you can then calculate the impedances of the components given their component values.

Good luck!

13. Jan 18, 2012

### Curious3141

Of course, assuming those are given in H (Henry) and Farad (F) won't make it a very realistic problem though, since those are HUGE inductances and capacitances respectively. It's really a rather badly presented problem, and it's best you seek clarification before wasting too much time/effort.

14. Jan 18, 2012

### andreasoro

Ok I will! Thanks so much! It was very nice of you!