Measuring volatge across capacitor with a not ideal oscilloscope

[connor02]

Homework Statement

A resistor (R) and a capacitor are connected in series to an AC supply. You are measuring the voltage across the capacitor with an oscilloscope. however, the oscilloscope is not ideal. you may model the oscilloscope as an ideal voltmeter in parallel with an internal resistance (r). What is the voltage across the capacitor during charging?

Homework Equations

I think the answer is V=Vo(r/(R+r))(1-e^(something))

but I don't know how to get here or what the e power is.

The Attempt at a Solution

I tried finding the impedence for the resistor and capacitor but that was wrong (apparently because of some phase difference).


Hope someone can help,
Connor

**EDIT**
I have just been given the answer and the something is -(R+r)t/(RrC)

so the answer is V=Vo(r/(R+r))(1-e^(-(R+r)t/(RrC)))

but I do not know how to arrive at it.

any help appreciated.

thanks.

 

[rude man]

Write the KVL equation (current into node v = current out of node v, where v = capacitor voltage). Have you had the Laplace transform? If not, this will be a differential equation & you have to know how to solve those (this is a simple first-order linear d.e. with constant coefficients).