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## Homework Statement

A capacitor of capacitance C is connected in paralell with a resistor of R ohms impedance. Calculate the size of the peak to peak voltage of the ripple produced relative to the peak output voltage V

_{p}.

## Homework Equations

Q=CV

dQ/dt = I

V=IR

V

_{c}=V

_{p}e

^{-t/RC}(am i allowed to use this in an AC circuit?)

or V

_{c}=-jI/R[itex]\omega[/itex]C

V = V

_{p}cos([itex]\omega[/itex]t)

## The Attempt at a Solution

Voltage drop across the resistor is just:

V = V

_{p}cos([itex]\omega[/itex]t)

Voltage drop across the capacitor can be aproximated to:

V

_{c}=V

_{p}(1-e

^{-t/RC})

The alteration to the equation in 2 is to ensure the capacitor voltage is 0 at t=0.

At t=0

V

_{R}- V

_{c}= V

_{p}

at t=T/2 or at 1/f

V

_{R}- V

_{c}= V

_{p}e

^{-1/fRC}

The ripple voltage will be the differance between these two:

V

_{Ripple}= V

_{p}(1-e

^{-/fRC})

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