yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

RC natural response example (3 of 3)


less than 1m read
·Nov 11, 2024

We just derived what the current is and the voltage. These are both the natural response of the RC. Now, what I did is I went ahead and I plotted out this using a computer, just using Excel to plot out what these two expressions look like. Let me show you that.

So, let's do a real quick example here with real values, just to see how this equation works. We'll say that this is 1,000 ohms; that's our resistor, and we'll say C is 1 microfarad. What we want to work out is R * C, which equals 10^3 ohms * 10^-6 farads, and that equals 10^(-3) seconds or 1 millisecond. That's the product of R and C.

I forgot the voltage; let's say we put two volts on this capacitor to start with like that. Now, we can say V of T equals V KN, which is 2 volts, times e^(-t/1 millisecond). That's our natural response for this particular circuit.

Now, let me show you what that looks like. This is V of T on this side equals 2 e^(-t/1 millisecond). You see it starts at 2 volts and then sags down as we predicted, and that's an exponential curve.

Then over here on this side, as we said before, it starts out at zero. The current in the capacitor is zero, and as soon as we throw open that switch, the charge charges over through the resistor. This is the equation here: I of T equals 2 volts over 1000 e^(-t/RC) or e^(-t/1 millisecond).

So, this is what we call the natural response of an RC circuit, and you'll run into this in almost every circuit you ever build.

More Articles

View All
The Monroe Doctrine
On December 2nd, 1823, US President James Monroe was giving his annual State of the Union Address to Congress when he threw in a couple of remarks about the United States’s relationship with the powers of Europe. He said, “The American continents, by the …
Alexander the Great conquers Persia | World History | Khan Academy
So, where we left off in the last video, we had Alexander the Great consolidating his power over the Macedonian Empire. In particular, he puts down a rebellion in Thebes, destroys the city, which makes the other city-states of Greece say, “Hey, we’re not …
Ron Howard and Brian Grazer Talk 'Genius' | National Geographic
I’m Ron. I’m Brian, and we’re here to talk to you about National Geographic’s first scripted show on genius. We’re focusing on Albert Einstein: 10 episodes that encompass his entire life. We, as contemporary people in this contemporary civilization that …
Identifying transformation described with other algebra and geometry concepts
We’re told that a certain mapping in the x-y plane has the following two properties: each point on the line ( y = 3x - 2 ) maps to itself. Any point ( P ) not on the line maps to a new point ( P’ ) in such a way that the perpendicular bisector of the segm…
How to Win (100 Cheat-codes for Life)
This video will change your life. Watch it as many times as you need. You’ll realize you hear something new every single time. Here are 100 cheat codes for winning at life. Welcome to alux.com, the place where future billionaires come to get inspired. You…
Re: Randyom Neuron (Reply to Everett)
Hey Randy, Um, I’m having a bit of trouble trying to explain myself in the comments, as you’ve probably noticed. So, this is a short video. Um, Everett’s requirement for free work for free will, or rather one of them, was that not only does the self have…