Time Constant for RC Circuit

[newyorkcity]

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:

C_total=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?

 

[gneill]

Not only are you on the right track, you've reached your destination!

 

[ashishsinghal]

That's correct

 

[newyorkcity]

thanks for your help guys, much appreciated.

 

[rwisz]

Your approach is on the right track. However, there are a few things to note:

1. The time constant (tau) for an RC circuit is defined as the product of the resistance and capacitance, not the sum. So the equation should be tau = RC, not tau = 5RC.

2. In this circuit, the capacitors are in parallel, so their equivalent capacitance is not simply the sum of their individual capacitances. Instead, you can use the formula for calculating the equivalent capacitance of capacitors in parallel, which is Ctotal = C1 + C2 + ... + Cn.

3. The internal resistance of the battery is negligible, so it can be ignored in the calculation of the time constant.

Taking these factors into account, the correct equation for the time constant of this circuit would be:

tau = (R * Ctotal) = (5R * 5C) = 25RC

So your final answer is correct, but you just need to make a few adjustments to your approach.