First Order RC Circuit Analysis: Homework Equations and Attempted Solution

[RoKr93]

Homework Statement

Homework Equations

v_c(t) = v_c(∞) + [v_c(0⁺) - v_c(∞)]*e^-t/τ (Voltage in a driven RC circuit)

τ = RC (time constant for an RC circuit)

The Attempt at a Solution

I'm pretty shaky with these sorts of problems and am quite unconfident of my work here. Step functions tend to confuse me and I'm not quite certain I interpreted this one right- I understand it to mean V_in(t) = V₀ when t ≤ τ. Also, my time constant appears to be inconsistent with the one given in the problem, but I'm not sure if it's supposed to be the same thing.

Would appreciate some clarification.

 

[szynkasz]

Your calculations are correct. What problems do you have?

 

[RoKr93]

Okay, great. I just haven't performed many of these problems and wasn't sure. But one question persists: why does my time constant differ from the given one? Is 6RC the time constant before t=0?

 

[szynkasz]

Yes, we have $\tau=6RC$ for $t<0$. But the circuit changes at $t=0$ so $\tau$ also changes.

 

[rezeew]

I would like to commend you for recognizing your areas of uncertainty and seeking clarification. It shows that you are committed to understanding the material and improving your skills in this subject.

To address your concerns, let's first clarify the meaning of the step function in this problem. The step function, Vin(t) = V0 when t ≤ τ, simply means that the input voltage is constant at V0 for the time period t ≤ τ. This is a common way to represent an input signal in circuit analysis problems.

Moving on to your time constant, it is indeed inconsistent with the one given in the problem. The time constant, τ = RC, is a property of the circuit and is determined by the values of the resistor (R) and capacitor (C). In this case, it seems that you have used a different value for either R or C, leading to a different time constant. I would suggest double-checking your calculations to ensure accuracy.

Finally, I would like to remind you that it is always helpful to check your solution by plugging in some values and seeing if it makes sense. For example, if you plug in t = 0, you should get Vc(0) = Vc(∞) + [Vc(0+) - Vc(∞)]*e^0 = Vc(∞) + [V0 - Vc(∞)] = V0, which is consistent with the given condition for t ≤ τ. This can help you catch any errors in your calculations and build confidence in your solution.

I hope this response helps clarify some of your concerns and builds your confidence in solving these types of problems. Keep up the good work in developing your skills as a scientist!