How can I solve the following problem: "Show that the voltage Vc (t)

across the capacitor as a function of time goes as 4.125(1 -

exp(-t/0.1375)) volts. When the steady state has been reached, what is

the power dissipated in each resistor and the energy stored in the

capacitor?"

Circuit diagram:

http://krebs.uk.com/rc.jpg
I know how to do this for a normal RC circuit, without the 22kOhm

resistor in parallel around the capacitor. I think I need to somehow use

Kirchhoff laws to figure this out, but I could really use a hand getting

started.

One way to look at it is that the cap is being fed from a voltage source

that has a series resistance of 10k || 22k, and a voltage that is equal to

the voltage divider voltage.

Notice that 6*22/(22+32) = 4.125, and that (10k||22k)*20e-6 = 0.1375.

If your textbook has mentioned Thevenin's theorem, that is simply the more

formal way to do this. It states that if you have a two-terminal

passive element in a circuit, you can find another circuit that consists

of the device, a single resistor, and a single current source,

all in series. The value of the voltage source is the thevenin equivalent

voltage, and the value of the resistor is the thevenin equivalent

resistance. The method to do this is trivial:

1) Remove the component you are analyzing from the schematic (in this case

C), and determine the voltage between the place where the leads previously

connected. In this case, it is V = 6 * (22/(10+22)). That is the thevenin

equivalent voltage.

2) Now, in that modified circuit, replace the voltage source with a wire,

and compute the resistance between those same two points. In this case, it

is 10k || 22k = 6.875k. This is the thevenin equivalent resistance.

Your circuit is then equivalent to

4.125V ------[6.875k ohms]------[20uF]-----GND

from the point of view of the cap, which is far easier to analyze.

Regarding the resistors, when the cap is in its 'steady state', it

effectively disappears from the circuit. So, use the equation for power

given voltage and resistance: (6-4.125)^2/10000 and 4.126^2/22000.

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Regards,

Bob Monsen

Nature does not at once disclose all Her mysteries. - Lucius Seneca (Roman

philosopher)