# Laplace Transform in an RC Circuit

#### juicebox4158

Joined Nov 18, 2012
4
i am soo lost that i dont known what u4 is for... if someone could walk me thought this. please... see attachment if the problem.

consider the RC circuit shown below with an exponentially decaying voltage source. The voltage is a
function of time as given below.

The voltage source turns on with a voltage of 2 at time t = 4 and then decays exponentially as t increases.

The differential equation for the voltage across the capacitor is

( ).

Suppose the initial voltage across the capacitor is ( ) . Taking the (unrealistic) values R = 1 and C =
1/3 and using V(t) given above, we have the initial value problem

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#### juicebox4158

Joined Nov 18, 2012
4

#### WBahn

Joined Mar 31, 2012
26,519
So why are you taking a class that assumes you have had Circuits if you haven't?

But, as I read the problem, I don't see where any knowledge of circuits is expected. You are GIVEN the differential equation that would normally come from performing a circuit analysis. And, like most math folks, completely ignores the fact that these are physical quantities that have units associated with them. But, be that as it may, you are simply being asked to solve a differential equation (the topic of this course) using Laplace transforms.

As for what u4 is for, that is almost certainly something that was covered in this course. Look it up in your text. Look for something like "unit step function". If you compare the equation for V(t) that they give with the verbal description provided around it, you should be able to figure out what the function u_4(t) has to look like.

#### juicebox4158

Joined Nov 18, 2012
4
the class does not have pre or co req of circuits but after playing around with it i think i found that the laplace transform is 2e^4u/s(s-2)^2...?