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### Course: Electrical engineering > Unit 2

Lesson 4: Natural and forced response- Capacitor i-v equations
- A capacitor integrates current
- Capacitor i-v equation in action
- Inductor equations
- Inductor kickback (1 of 2)
- Inductor kickback (2 of 2)
- Inductor i-v equation in action
- RC natural response - intuition
- RC natural response - derivation
- RC natural response - example
- RC natural response
- RC step response - intuition
- RC step response setup (1 of 3)
- RC step response solve (2 of 3)
- RC step response example (3 of 3)
- RC step response
- RL natural response
- Sketching exponentials
- Sketching exponentials - examples
- LC natural response intuition 1
- LC natural response intuition 2
- LC natural response derivation 1
- LC natural response derivation 2
- LC natural response derivation 3
- LC natural response derivation 4
- LC natural response example
- LC natural response
- LC natural response - derivation
- RLC natural response - intuition
- RLC natural response - derivation
- RLC natural response - variations

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# RC step response example (3 of 3)

An example solution of an RC step response, with real component values. Created by Willy McAllister.

## Want to join the conversation?

- At0:49, at the schematic diagram what does that circle with an inverted Z mean....and what is Step Response?(2 votes)
- The circle is the voltage source. That backwards Z is just a representation of the waveform that it generates. Step response is the reaction of a circuit to a step in voltage, in this case, the reaction of an RC circuit to an instantaneous step in voltage produces a waveform that increases at an exponential decay.(6 votes)

- I know it's very simply to do, but I think people would benefit from taking the derivative of Q = CV, so that dq/dt = i, and dv/dt is just the derivative of the step response, and then plotting how the current changes as well. Perhaps making a separate video in which you do this for inductors as well and put all four plots side by side would be cool! (V_c, I_c, V_L, I_L).(2 votes)
- At3:00you changed Vs to 1.2V, but you didn't change Vs to 1.2V at the end of the formula. To match the plot, Vs is 1.2V in all places, correct?(1 vote)
- That's correct. The last term of the equation should be +1.2V.

You should be seeing a note at the bottom of the video screen that points out the goof.(2 votes)

- does the exponential curve due to the time of charging of the capacitor?(1 vote)
- The exponential shape is due to charging the capacitor
*through a resistor*.(1 vote)

- Hi, I solved the differential equation " CV'+V/R=Vs/R " using a constant of integration to find V(t). For some reason I do not seem to get the same answer as you. It seems like this should be a valid approach. My integration constant ended up being e^*(t/rc). Not sure what I am doing wrong. Edit: I figured it out, I was leaving out a constant of integration.(1 vote)
- Hi there,how about with the step response for parallel RC circuit,is that same as the series one?(1 vote)
- The parallel version of the RC step is a strange circuit if you are talking about one with a voltage source in parallel with a resistor in parallel with a capacitor. The voltage source determines the voltage on the R and C. The voltage source and the R determine the current in the resistor (Ohm's Law). And the steepness of the voltage step (dv/dt) and the value of C determines the current in the capacitor. i_c = C dv/dt. If the voltage step is mathematically instantaneous then dv/dt is infinity and so is the capacitor current for just a moment.

When you do the parallel RC step response what you want to do is change out the voltage source for a current source, and give the circuit a step of current. In that case, you get an e^t/RC curve for the voltage as with the series RC. The height of the voltage step is determined by I_s times R.(1 vote)

- at1:21, how did you get +3 and -6?(1 vote)
- The +3 comes from interpreting the "k" (kilo) prefix on the resistor value as 10^3.

The -6 comes from the "u" (micro) prefix, 10^-6.(1 vote)

## Video transcript

- [Voiceover] In the
last video, we worked out the step response of an RC circuit, and now we're gonna
look at a real example. So, this is our answer,
this is the step response, the total response to our
circuit, to a step input. And what does this look like? Well, I'm gonna move down a little bit. We'll make up a circuit and
we'll do a real example here. Let's say we do a step, and the step goes from .2 volts up to, say 1.1 volts. And let's let R equal one K, ohm. K, ohm. And let the capacitor
equal four microfarads. So now let's plug these values
over here into our solution and see what we get. Now, first I'm gonna work out RC. RC is equal to one K, ohm times four microfarads. And what does that equal? K is plus three. And micro is minus six. So one times four is four. And plus three minus six is times 10 to the minus three. And that is in seconds, so that's equal to four milliseconds. Now, let's plug the rest
of our values in here. V of T. The total response, or the step response equals v naught, .2, minus V, S, that's the step voltage, 1.1, times e to the minus t over four milliseconds plus V, S. V, S is 1.1. So I went ahead and I plotted this using a computer, and we'll
see how close this comes to what we sketched earlier. So here's V, T. Or, the step response, the total response of our RC network to a step voltage. The step voltage is here in rose color. And it goes from .2 volts up to, ooh, I got it wrong. 1.2 volts, let's change
that to the right number. 1.2, 1.2. And this is what it looks like. And if you go back and
compare this to what we saw, what we sketched at the beginning, it'll look pretty similar. So, the output voltage, the
voltage on the capacitor here, starts at V naught, which is .2, it ends up at V, S, which
is 1.2 in this case, and that's the forced response up here. And in between, it did that
smooth exponential curve. That's what the step response
of an RC circuit looks like.