Circuit with resistor, switch and capacitor

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The discussion revolves around analyzing a circuit containing a battery, resistors, a switch, and a capacitor. Participants explore how to determine the current through the resistors and the charge on the capacitor over time using Kirchhoff's laws and differential equations. They emphasize the importance of understanding initial and steady-state conditions for the capacitor, noting that it behaves like an open circuit when fully charged. The time constant for the circuit is derived from the equivalent resistance seen by the capacitor, which is calculated based on the configuration of the resistors. Overall, the conversation highlights the complexities of RC circuits and the need for foundational knowledge in circuit analysis.
  • #61
Yup. Looks good.
 
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  • #62
This is great!

But you mentioned in post #13
gneill said:
That is the "starting from the basics" approach, yes.

The thing is this, in the next task I'm asked to verify the result using a numerical method; ie. using a differential equation! (forward Euler for instance)

But I/we have solved it, by simply assuming the "form" of the function; I guess I am puzzled by the "starting from the basics" approach" you mentioned...

How does one go about finding the differential equation?
 
  • #63
johann1301h said:
How does one go about finding the differential equation?
One writes the circuit equations using the differential or integral forms for the capacitor voltage or current, then solve the resulting differential equation. So for example, for the simple case of a charged capacitor discharging through a resistor, writing KCL:

##C \frac{dV}{dt} +\frac{V}{R} = 0##

##\frac{dV}{dt} = -\frac{V}{R C}##

##\frac{dV}{V} = -\frac{dt}{R C} ##

and so on
 

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