How Do I Solve for Both c and r in a Complex Impedance Equation?

[zekester]

i have an equation ((r^2)*(-i/(w*c)))+(r/(w*c))
divided by (r^2) + (1/(wc)^2)
equals -951 - (i*13026)

where i is the square root of negative one and w is known. How do I get two equations to solve for both c and r.

 

[arildno]

Assuming "r" and "c" to be real numbers, equate the real parts in your equation, and the imaginary parts in your equation:
$$\frac{\frac{r}{wc}}{r^{2}+\frac{1}{(wc)^{2}}}=-951$$
And:
$$-\frac{\frac{r^{2}}{wc}}{r^{2}+\frac{1}{(wc)^{2}}}=-13026$$

 

[wais]

To solve for both c and r, you can use the following steps:

1. Multiply both sides of the equation by the denominator (r^2 + (1/(wc)^2)) to get rid of the fraction on the left side.

2. Simplify the left side by using the distributive property. This will give you a new equation with only c and r variables.

3. To get two equations, you can substitute different values for r and c in the new equation. For example, you can substitute r=0 and solve for c, then substitute c=0 and solve for r. This will give you two equations with one variable each.

4. Once you have the two equations, you can solve them simultaneously using algebraic methods such as substitution or elimination.

Alternatively, you can also use a system of equations solver or a graphing calculator to solve for both c and r simultaneously.