I know that to solve:
f=1 over 2 pi sqrt LC for C, I have to use
C= 1 over L(2 pi f)^2
Can someone take me through the rearranging please. Thanks.
f*2PI = 1/sqrtLC
square both sides
(f*2PI)^2=1/LC
multiply both sides by C, divide both sides by (f*2PI)^2
f = 1/[2*pi*sqrt(LC)],
square both sides.
f^2 = 1/[4*pi^2*LC].
Cross multiply.
4*pi*2*LC*f^2 = 1
solve for C.
C = 1/[4*pi^2*f^2*L]
C = 1/[(2*pi*f)^2*L]=
1/L*(2*pi*f)^2
Thank you very much.
C=1/4perr square fsquare l
To rearrange the formula f=1/(2π√LC) to solve for C, you need to isolate the variable C on one side of the equation.
1. Start with the original equation: f = 1/(2π√LC).
2. Multiply both sides of the equation by 2π√LC to get rid of the denominator on the right side: f × 2π√LC = 1.
3. Next, square both sides of the equation to remove the square root: (f × 2π√LC)^2 = 1^2.
4. Simplify the left side of the equation: (f^2) × (2π)^2 × L × C = 1.
5. Divide both sides of the equation by (f^2) × (2π)^2 × L to isolate C: C = 1/[(f^2) × (2π)^2 × L].
6. Rearrange the terms in the denominator to write it in a more standard form: C = 1/[4π^2Lf^2].
Therefore, the rearranged formula is C = 1/[4π^2Lf^2].
Note that the rearranged formula represents an equation to calculate the value of capacitance (C) based on the values of frequency (f) in Hertz, inductance (L) in Henrys, and π (pi) as a mathematical constant.