Hi,
I'm doing homework to study for my final exam tomorrow. The final will contain RC, RL, and RLC circuits. I have the solution to problem 7.21 in Nilsson Riedel (sounds like they'd write a circuits book, huh?) but it doesn't click with me.

As I understand it, parallel capacitors equivalent capacitance is calculated by adding the capacitances.

In this example there are two capacitors of 2 microFarads and 8 microFarads separated by a 5 kiloOhm resistor.

My professors solution calculates the time constant by calculating the equivalent capacitance, but he does (8*2) / (8+2). Would it not just be 10 microFarads? He's probably correct. Are they in series because of the resistor?

Here's a picture of the solution, the bottom part is what the circuit looks like after the switch is closed with the two capacitors and the resistor.

 

To calculate the time constant of an RC loop, you must reduce it to a single resistance and capacitance. Isn't it rational to add in series two capacitors that share only one common end? Clearly C1 and C2 are connected in series.

 

Thanks Georacer. I just had a lightbulb go off. I think my circuits were fried when I asked this question.

 

You 're wellcome.