## Half wave rectifier Ripple Voltage

1. The problem statement, all variables and given/known data

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 Vp.

2. Relevant equations

Q=CV
dQ/dt = I
V=IR
Vc=Vpe-t/RC (am i allowed to use this in an AC circuit?)
or Vc=-jI/R$$\omega$$C

V = Vpcos($$\omega$$t)

3. The attempt at a solution

Voltage drop across the resistor is just:

V = Vpcos($$\omega$$t)

Voltage drop across the capacitor can be aproximated to:

Vc=Vp(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

VR - Vc = Vp

at t=T/2 or at 1/f

VR - Vc = Vpe-1/fRC

The ripple voltage will be the differance between these two:

VRipple= Vp(1-e-/fRC)

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