32.76 Time for current to decay with capacitors and resistors

  • #1

Homework Statement


The capacitors in the figure are charged and the switch closes at t=0s. At what time has the current in the 8 ohm resistor decayed to half the value it had immediately after the switch was closed?
(The circuit looks something like this; 2 capacitors are in series at 60microfarads each, another is in parallel with the other two at 20microfarads. Above and to the right is a switch, and to the right of the switch is an 8 ohm resisitor. Below and to the right of the 8 ohm resistor is two resistors in parallel, one at 30 ohm and another at 20 ohms.)

Homework Equations


Q=Qoe^(-t/RC)
I=Ioe^(-t/RC)
From knight edition 2, a strategic approach

The Attempt at a Solution


Value of capacitors=50*10^-6 F
Value of resistors= 23 ohms
Using I=Ioe^(-t/RC)
(We dont really need to find the values of I and Io because we know that the current has to decay to 1/2 its original value
ln(0.5)= (-t/RC)
I think my point of error lies here, but im not sure...
ln(0.5)= (-t/(8ohms*(50*10^-6)))
-t=2.77*10^-4 s
This answer is incorrect. Considering that the textbook calls this a challanging problem, im assuming that there is more work needed to answer this question than what I have done. Can someone please help me?
 

Answers and Replies

  • #2
You need to use equivalent resistance when finding RC, not the 8 Ohms.
 
  • #3
gneill
Mentor
20,925
2,866
You need to use equivalent resistance when finding RC, not the 8 Ohms.
The Original Post is from 2010. It is rather unlikely that the Original Poster (who was last active here back in April of 2010) is still interested in this particular problem.

If you wish to pursue the solution of the problem, feel free to provide an analysis. A circuit diagram of your understanding of the circuit involved would be beneficial for helpers who wish to chime in.
 

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