# Laplace Transform on RC circuit

• Engineering
• CoolDude420
In summary, the conversation was about solving a problem involving partial fraction expansion and finding the voltage across a capacitor in a series circuit. The initial charge on the capacitor was not specified, but it was assumed to be 0. The next step was to use algebra and inverse Laplace tables to solve for the coefficients A and B. A helpful resource for solving partial fraction expansion was provided.
CoolDude420

## The Attempt at a Solution

I'm kind of lost now, how do I go about getting this into the right form for partial fraction exapnsion. And also what do I do with the V(0'). There was no information given about it.

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What is the problem statement? It is not clear from what you supplied. Also, why do you have an initial charge on the capacitor when the switch was initially open?

The problem is to find v(t) for t>0. The diagram is a series combination of a voltage source E, resistor R and capcitance C. Where v(t) is the voltage across the capacitor. The step function diagram is for E not v(t)

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CoolDude420 said:
I'm kind of lost now, how do I go about getting this into the right form for partial fraction exapnsion.
Algebra.
And also what do I do with the V(0'). There was no information given about it.
It's reasonable to assume it's equal to 0, though the problem statement really should have included information about it.

vela said:
Algebra.

It's reasonable to assume it's equal to 0, though the problem statement really should have included information about it.

Any idea on what next "algebra" step to take?

take a look at any inverse laplace table. You need to find a way to get your system into one of those forms.
So...

E/C / [ S * (Rs+1/C) ] = A1 + [A2 / S] + [A3 / (Rs+1/C)]

Solve for A and B. How do you do that. Try setting s=0 and s= -1/(RC), which will cancel out the values

## What is Laplace Transform on RC circuit?

Laplace Transform is a mathematical tool used to analyze the behavior of a system over time. In the context of RC circuits, it is used to study the relationship between voltage and current in a circuit with a resistor and a capacitor.

## How is Laplace Transform used in RC circuits?

In RC circuits, Laplace Transform is used to convert a differential equation into an algebraic equation, making it easier to solve. This allows us to determine the behavior of the circuit in the frequency domain, rather than the time domain.

## What are the benefits of using Laplace Transform on RC circuits?

The use of Laplace Transform on RC circuits allows for easier analysis and calculation of the circuit's behavior. It also helps in designing and optimizing the circuit for specific applications.

## What is the relationship between Laplace Transform and impedance in RC circuits?

Laplace Transform and impedance are closely related in RC circuits. The impedance of a circuit is the Laplace Transform of its input voltage divided by the Laplace Transform of its output current. This relationship allows us to calculate the impedance of a circuit using Laplace Transform.

## What are some real-life applications of Laplace Transform on RC circuits?

Laplace Transform on RC circuits has many practical applications, such as in electronic filters, signal processing, and control systems. It is also used in analyzing and designing power distribution systems and in studying the behavior of biological systems.

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