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Switch 1 is turned on until the 12 microF capacitor is completely charged. Then Switch 1 is switched off, while switch 2 is switched on.

How do you write a differential equation that may be used to find charge on the 4 mircroF capacitor as a function of time?

My attempt:

Applying Kirchhoff's Loop Rule: [tex]0 = V_1 - R_1 \frac{dq}{dt} - R_2 \frac{dq}{dt} - \frac{q}{C_2}[/tex], where q is the charge on the 4 microF capacitor.

This can be rewritten as

[tex]0 = \frac{Q-q}{C_1} - \frac{dq}{dt} (R_1 + R_2)- \frac{q}{C_2}[/tex]

In this last step I assumed the charged discharged from the 12 microF capacitor is the charge that appears on the 4 microF capacitor.

(loops used are clockwise)

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# Homework Help: Charging a Capacitor with Another Capacitor

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