Analyzing Parallel RC Circuits with Time Constant Variation

AI Thread Summary
To analyze the time constant of a parallel RC circuit when the switch is on, one must derive a differential equation using Kirchhoff's laws to determine the charge on the capacitor. The time constant can be identified within this equation. A recommended approach is to find the Thevenin equivalent sources for the circuit when the switch is open and closed, simplifying the analysis into two distinct RC circuits. Understanding the charging equation is crucial for calculating the capacitor's potential at a specific time, such as t=2s. This method provides clarity on the behavior of the circuit under varying conditions.
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the attached file is the question

I know the time constant after opening the switch

but how can i know the time constant when the switch is on?

This is NOT the classic initial and AFTER A LONG LONG LONG Time question

How can i know the potential of C in t=2s ?

What is the equation for charging ?

Plz help, i googled for a long time but still can't get the ans
 
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What is the equation for charging ?
With Kirchhoff's laws, you can get a differential equation for the charge of the capacitor. The time constant can be seen in this equation.
 
One approach would be to find the Thevenin equivalent sources that the capacitor "sees" when the switch is open and when the switch is closed. That'll give you two simple RC circuits to work with...
 

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