# How to express this equation in terms of v?

I read from my physics textbook that the magnitude of a ripple voltage decreases if the capacitance is increased in a rectifier circuit, but the textbook didn't specify what the exact mathematical relationship is between those two.

While trying to determine this, I encountered an equation that I have been unable to solve: $$\ln\left(\frac{V}{P}\right)=\frac{-cos^{-1}\left(-\sqrt{\frac{V^2}{P^2}}\right)}{2πfRC}$$ which needs to be expressed in terms of V. I'm not sure how I should continue, since it has natural log and arccos on different sides.

• No hope to express the solution in terms of a finite number of standard functions. Use numerical calculus. – JJacquelin Sep 12 '15 at 10:36

There's no way to write this as an explicit function of $V$. The natural log/arccos pair is a pretty damning thing to run into in an equation. This must be numerically approximated.