Given the formula Xc=1/6.28fC, find C if Xc =500 and f=2000.
What are the rules that take me from 500/1 = 1/6.28*2000*C to the next step of: C=1*1/500*6.28*2000 ?
The * is showing a multiplication sign. The number before / is the numerator and after is the denominator. This has to do with proportions and cross products but I am not understanding the rules/principles here.
easy...
capreactance=(1/(2PI*f*C)
multiply each side by C, and divide by capreactance.
C=1/(2PI*f*Xc)
To find C using the formula Xc = 1/(6.28fC) and given that Xc = 500 and f = 2000, you would follow these steps:
1. Substitute the given values into the equation: Xc = 1/(6.28 * f * C)
Xc = 500,
f = 2000
So the equation becomes: 500 = 1/(6.28 * 2000 * C)
2. Multiply both sides of the equation by (6.28 * 2000 * C) to isolate C on one side.
500 * (6.28 * 2000 * C) = 1
3. Simplify the left side of the equation by multiplying:
500 * (6.28 * 2000 * C) = (500 * 6.28 * 2000 * C)
4. On the right side, simplify the expression:
(500 * 6.28 * 2000 * C) = (1 * 1)
5. Divide both sides of the equation by (500 * 6.28 * 2000):
(500 * 6.28 * 2000 * C) / (500 * 6.28 * 2000) = (1 * 1) / (500 * 6.28 * 2000)
This step cancels out the term (500 * 6.28 * 2000) on the left side.
6. Simplify the equation:
C = 1 / (500 * 6.28 * 2000)
Now, you can further simplify the equation if desired, by multiplying and dividing:
C = 1 * (1 / (500 * 6.28 * 2000))
C = 1 / (500 * 6.28 * 2000)
C = 1 / (6280000 * 500)
C = 1 / 3.14 × 10^9
So, C equals approximately 3.18e-10, which is equivalent to 0.318 pF (picofarads).
In summary, the rules used to get from the equation Xc = 1/(6.28fC) to C = 1 / (500 * 6.28 * 2000) are:
1. Multiply both sides of the equation by (6.28 * 2000 * C).
2. Simplify the left side of the equation and simplify the right side by multiplying.
3. Cancel out the term (500 * 6.28 * 2000) by dividing both sides of the equation.
4. Further simplify the equation if desired by multiplying and dividing.
5. Calculate the final value of C.