 #1
Felipe Lincoln
Gold Member
 99
 11
Problem: At the instant ##t=0## the capacitor C1 has a charge ##Q_0>0## and the capacitor C2 has no charge. (I forgot to draw the switch to close and open the circuit), so the switch is closed and the current start flowing. Let the circuit goes to ##t\to\infty##. a) What's the energy stored in each capacitor? b) How does the current vary over time? c) What's the power dissipated in each resistor at an instante ##t>0## ?
How I'm trying: The energy in each capacitor would be ##\frac{1}{2}CV_F^2## and this ##V_F## will be the same in both capacitor because there will be no current flowing once there's no moving charge. Ok, but how can I find this ##V_F##? I had no success on trying kirchhoff mesh law because I ended with two function of charge over time and couldn't solve the differential equation. $$\dfrac{Q_1(t)}{C_1} = (R_1+R_2)i(t) + \dfrac{Q_2(t)}{C_2}$$
Here is where I stopped, can't get any further than this.
How I'm trying: The energy in each capacitor would be ##\frac{1}{2}CV_F^2## and this ##V_F## will be the same in both capacitor because there will be no current flowing once there's no moving charge. Ok, but how can I find this ##V_F##? I had no success on trying kirchhoff mesh law because I ended with two function of charge over time and couldn't solve the differential equation. $$\dfrac{Q_1(t)}{C_1} = (R_1+R_2)i(t) + \dfrac{Q_2(t)}{C_2}$$
Here is where I stopped, can't get any further than this.
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