First Order Transient: RC Circuit

[jclay06]

Homework Statement

http://i.thespiffylife.com/files/1/trans1.jpg

i have to find Vc(t)

Homework Equations

I know that Vc(0+) = Vc(0) = Vc(0-) and Vc = Vs*e^(-t/RC)

The Attempt at a Solution

What I'm unsure on is what the equivalent resistance of the circuit would be so I could find the time constant. I know since the Capacitor is fully charged it now behaves as a voltage source, but for any nodal / mesh equation I come up with I'm always one equation short of having equal unknowns & equations.
So ... any help on how to find the Req would be nice.

 

[MATLABdude]

Homework Statement

http://i.thespiffylife.com/files/1/trans1.jpg

i have to find Vc(t)

Homework Equations

I know that Vc(0+) = Vc(0) = Vc(0-) and Vc = Vs*e^(-t/RC)

The Attempt at a Solution

What I'm unsure on is what the equivalent resistance of the circuit would be so I could find the time constant. I know since the Capacitor is fully charged it now behaves as a voltage source, but for any nodal / mesh equation I come up with I'm always one equation short of having equal unknowns & equations.
So ... any help on how to find the Req would be nice.

Find the Thévenin equivalent around the capacitor.

EDIT: Before, or after t=0? Which will affect the time constant?

 

[Mene]

I would suggest approaching this problem by breaking it down into smaller, more manageable steps. First, let's review the basics of RC circuits. A first order RC circuit is a circuit that contains a resistor (R) and a capacitor (C) in series. When a voltage (Vs) is applied to the circuit, the capacitor begins to charge and the voltage across the capacitor (Vc) increases. This increase in voltage is not instantaneous, but rather follows an exponential curve. The time it takes for the voltage to reach a certain percentage (usually 63.2%) of its final value is known as the time constant (τ) and is equal to the product of the resistance and capacitance (τ = RC).

Now, to solve for Vc(t), we can use the equation Vc = Vs*e^(-t/RC). However, as you mentioned, we need to know the equivalent resistance (Req) of the circuit in order to find the time constant. In this case, we can find Req by using the parallel resistance formula, which states that the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances (1/Req = 1/R1 + 1/R2). In this circuit, the 10kΩ resistor and the 10kΩ resistor are in parallel, so we can use this formula to find the equivalent resistance:

1/Req = 1/10kΩ + 1/10kΩ = 2/10kΩ
Req = 5kΩ

Now, we can use this value of Req to find the time constant:

τ = RC = (5kΩ)(10μF) = 50ms

Finally, we can use the equation Vc = Vs*e^(-t/RC) to solve for Vc(t) at any given time t.

I hope this explanation helps you to better understand how to approach this problem. Remember to always break down complex problems into smaller, more manageable steps and to use the appropriate equations and formulas. Good luck with your homework!