Charge on capacitor (RC circuit)

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SUMMARY

The discussion focuses on analyzing the behavior of an RC circuit involving a capacitor and resistors after a switch is closed and then reopened. Key findings include that after a long time, the currents through the resistors are I6 = 1A, I8 = 1.5A, and I12 = 0.5A. The voltage across the capacitor is determined to be 6V, which is critical for calculating the charge and current immediately after the switch is reopened. The time constant of the capacitor discharge is calculated using the formula RC, where R is the equivalent resistance and C is the capacitance.

PREREQUISITES
  • Understanding of RC circuit behavior
  • Familiarity with Ohm's Law (V = I Req)
  • Knowledge of capacitor charge equations (Q = CV)
  • Basic principles of circuit analysis without Kirchhoff's rules
NEXT STEPS
  • Calculate the time constant for different RC circuits
  • Explore the effects of varying resistance values on capacitor discharge
  • Learn about transient analysis in electrical circuits
  • Investigate the role of capacitors in filtering applications
USEFUL FOR

Students studying electrical engineering, circuit designers, and anyone interested in understanding the dynamics of RC circuits and capacitor behavior.

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Homework Statement


1) Determine the current in each resistor and charge on the capacitor after a long time immediately after the switch is closed
2) Determine the current in each resistor and charge on the capacitor after a long time

After the switch has been closed for a long time it is re-opened.

3) Determine the current in each resistor and the charge on the capacitor immediately after the switch has been re-opened.
4) Determine the time constant of the capacitor discharge.

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Homework Equations


V = I Req
Q = CV

The Attempt at a Solution


I got #1 and got I6 = 1A, I8 = 1.5A, and I12 = .5A
I'm not sure what to do about #2 though. What is the voltage across the capacitor? I thought it would be 6V, because that is the voltage across the parallel series. However, there is a voltage drop after the 1A current runs across the 6ohm resistor so the V across the capacitor is 0.

For #3 and 4, does the 8ohm resistor come into play or no?
Thanks for the help guys.
 
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Is the V across the capacitor just 6V? If so I think I'm good. #2 I through the 6ohm resistor is 0, then I through the other two resistors is 18V/20ohms right?
#3 I = 6V/18ohms Q= 28 E-6 * 6
#4 (18 * 28E-6) = RC
 
Voltage which charges the capacitor is the voltage across 12 ohm resistance. Calculate that voltage.
When the capacitor is completely charged, the same voltage will be the voltage across it.
 
oh is this Kirchoff's rule?
 
No. There is no need to apply Kirchhoff rule.
 

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