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.