How Is the Time Constant Calculated in a Series-Parallel RC Circuit?

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The time constant for the given series-parallel RC circuit is calculated using the formula tau = RC. In this case, the circuit has five resistors in series, leading to an equivalent resistance of 5R. The five capacitors are in parallel, resulting in a total capacitance of 5C. Therefore, the overall time constant is tau = 25RC. The calculations confirm that the approach taken to determine the time constant is correct.
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Homework Statement



What is the time constant of the circuit shown in the figure? Each resistor has resistance R, and each capacitor has capacitance C. Internal resistance of the battery is negligible.

See the attached figure.


Homework Equations



tau=RC


The Attempt at a Solution



I assume that the R term has a coefficient of 5, due to the 5 resistors in series each with resistance R. I am confused about the capacitors. Since they are parallel, I assume that I can convert to the equivalent capacitor:

Ctotal=C1+C2+C3+C4+C5

resulting capacitance is 5C. So with terms of 5R and 5C, I get:

tau=25RC

am I on the right track?
 

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Not only are you on the right track, you've reached your destination!
 
That's correct :smile:
 
thanks for your help guys, much appreciated.
 

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