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
Decomposing angles | Math | 4th grade | Khan Academy
What is the measure of angle EAC? So, we have this symbol here which means angle and then these three letters: E, A, C. Now, to measure angle EAC, we need to first find angle EAC down here on our picture. The way we can do that is use these three letter…
Spotting Ecommerce Trends in Shipping Data - Laura Behrens Wu
How about we just start with a quick intro? Cool. Yeah, thanks for having me! My name is Laura. I run a company called Shippo. We power shipping for e-commerce. What that means is we connect our customers, who are e-commerce stores, platforms, and marketp…
Can We Fix Climate Change? | Explorer
We can’t really fix climate change. We can mitigate it. We can get to work on it. We can spread it out. We can make things better. What we got to do is stop burning fossil fuels immediately, as soon as we possibly can. Then there’s a strange effect that …
Warren Buffett: How Inflation Will Impact the Stock Market (2021)
It’s no secret that inflation is top of mind for investors right now, as prices for housing, lumber, copper, steel, and countless other commodities and goods increase at the fastest rate in years. It is natural for an investor to wonder how inflation can …
Harry Zhang with Kevin Hale on Building Lob to Automate the Offline World
Today we have Harry Zhang, co-founder of Lob. Lob makes APIs for companies to send letters and postcards. So, Kevin has a question for you. “I’m trying to think back to when you guys applied to YC. You didn’t have almost anything. Like, I would say it wa…
Nintendo FURNITURE??? -- Mind Blow #15
A real Zelda Treasure chest? And coming soon from 7-Eleven: two cups, one straw. Vsauce, Kevin here. This is Mind Blow. A few years we were treated to a functioning NES controller coffee table. Well, here’s a brand new one with custom NES art and a place…