- #1

Mutaja

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## Homework Statement

Given the attached circuit, compute Tau, U

_{C1}(t) and U

_{C1}(∞).

Then assume t = ∞ and C1 has the potential of E

_{th}. Put the switch in the other position, so that C1 can discharge through R3. C2 will, of course, charge until U

_{C1}= U

_{C2}.

Compute Tau, U

_{C1}(t), U

_{C2}(t) and I

_{R3}(t).

From these calculations, it should be simple to graph it using the y-axis as U or I and the c axis as Tau (time (s)).

## The Attempt at a Solution

First things first. I attached the whole problem, since it's related to one circuit.

Compute Tau, U

_{C1}(t) and U

_{C1}(∞).

I started with transforming the circuit into a thevenin equivalent.

R

_{TH}= R1||R2 = 2350Ω.

E

_{TH}= E

_{R2}= [itex]\frac{R2 * E}{R1 + R2}[/itex] = [itex]\frac{4700Ω * 8V}{4700Ω + 4700Ω}[/itex] = 4V.

Tau = R*C = 2350Ω * 680*10

^{-6}F = 1.598S

U

_{C1}(t) = E

_{TH}(1-e

^{[itex]\frac{-t}{Tau}[/itex]}) = 4V * (1-e

^{[itex]\frac{-t}{1.598S}[/itex]})

U

_{C1}(∞) is my first problem, assuming the above is correct. By infinity, do they mean when C1 is fully charged? From earlier, I think 5 Tau used to be the definition of a fully charged capacitor, but this may be completely wrong, and knowing me, it is.