Question

Hi, heres a problem I am trying to do in MATLAB. s = (-1/2*R*C) + a*((1/2*R*C)^2 - (1/L*s))^1/2 . My roblem is how can I solve this is s is on both sides of equation??

Answer 1

s = (-1/2*R*C) + a*((1/2*R*C)^2 - (1/L*s))^1/2

Answer 2

and I am given all values except s

Answer 3

@ganeshie8

Answer 4

You have
$$
s=-\frac{C R}{2}+a \sqrt{\left(\frac{R C}{2}\right)^2-\frac{s}{L}}
$$
Therefore, after rearranging terms,
$$
\begin{array}{l}
\text{With } ~L\neq 0,~ a\neq 0 \\
s=\frac{-\sqrt{a^2 \left(a^2+C^2 L^2 R^2+2 C L R\right)}-a^2-C L R}{2 L} \\
\end{array}
$$

Answer 5

Im a little confused as to what you did there.......

Answer 6

I dont think I wrote my equation very cleary.....this was a matlab problem. I think I might open the question again with some slight adjustments..

Answer 7

and I think it should be s= -1/2RC....

Answer 8

$$
s=-\frac{C R}{2}+a \sqrt{\left(\frac{R C}{2}\right)^2-\frac{s}{L}}\\
s+\frac{C R}{2}=a \sqrt{\left(\frac{R C}{2}\right)^2-\frac{s}{L}}\\
(s+\frac{C R}{2})^2=a^2\left ( \cfrac{R C}{2}\right )^2-\frac{s}{L}\\
s^2+CR+\cfrac{(CR)^2}{4}=a^2\left ( \cfrac{R C}{2}\right )^2-\frac{s}{L}\\
s^2+\frac{s}{L}+\cfrac{(CR)^2}{4}-a^2 \cfrac{(R C)^2}{4}=0\\
s^2+\frac{s}{L}+\cfrac{(CR)^2}{4}(1-a^2)=0
$$
Now use quadratic formula.

Answer 9

Solve for s:
s^2+s/L+1/4 C^2 R^2 (1-a^2) = 0

Solve the quadratic equation by completing the square.

Subtract 1/4 (1-a^2) C^2 R^2 from both sides:
s^2+s/L = -1/4 (C^2 R^2 (1-a^2))

Take one half of the coefficient of s and square it, then add it to both sides.

Add 1/(4 L^2) to both sides:
s^2+s/L+1/(4 L^2) = 1/(4 L^2)-1/4 C^2 R^2 (1-a^2)

Factor the left hand side.

Write the left hand side as a square:
(s+1/(2 L))^2 = 1/(4 L^2)-1/4 C^2 R^2 (1-a^2)

Eliminate the exponent on the left hand side.

Take the square root of both sides:
s+1/(2 L) = sqrt(1/(4 L^2)-1/4 C^2 R^2 (1-a^2)) or s+1/(2 L) = -sqrt(1/(4 L^2)-1/4 C^2 R^2 (1-a^2))

Look at the first equation: Solve for s.

Subtract 1/(2 L) from both sides:
s = sqrt(1/(4 L^2)-1/4 C^2 R^2 (1-a^2))-1/(2 L) or s+1/(2 L) = -sqrt(1/(4 L^2)-1/4 C^2 R^2 (1-a^2))

Simplify powers and products.

Combine C^2 and R^2 under the same power:
s = sqrt(1/(4 L^2)+1/4 C^2 R^2 (a^2-1))-1/(2 L) or s+1/(2 L) = -sqrt(1/(4 L^2)-1/4 C^2 R^2 (1-a^2))

Look at the second equation: Solve for s.

Subtract 1/(2 L) from both sides:
s = sqrt(1/(4 L^2)+1/4 C^2 R^2 (a^2-1))-1/(2 L) or s = -1/(2 L)-sqrt(1/(4 L^2)-1/4 C^2 R^2 (1-a^2))

Simplify powers and products.

Combine C^2 and R^2 under the same power:

Answer:
s = sqrt(1/(4 L^2)+1/4 C^2 R^2 (a^2-1))-1/(2 L) or s = -1/(2 L)-sqrt(1/(4 L^2)+1/4 C^2 R^2 (a^2-1))