Two capacitors, one resistor and an ideal battery are connected through switches s1,s2 and s3 as shown in figure. Initially capacitor of capacitance 4C is charged, while other is uncharged. The upper plate of capacitor 4C is positive plate. Now, switches s1,s2 and s3 are closed simultaneously then find current in resistor and charge on capacitor 6C as a function of time. question

This is not a homework question. I tried to find the current by first integrating and then differentiating but couldn't get the correct answer. I know about the formulae to be used. I formed 4 equations :


-(4q0+q2)/4C -iR +e =0



Where q1 is the charge on 6C at time t and q2 is the extra charge on q2 at time t.

  • $\begingroup$ You can solve this problem by considering the charges, voltages and currents at t=0. $\endgroup$ – Farcher Feb 6 '16 at 20:40
  • $\begingroup$ @Farcher but the question is asking to find as a function of time $\endgroup$ – Utkarsh Barsaiyan Feb 7 '16 at 11:03
  • $\begingroup$ That did not escape my notice but did you notice that the time dependence is the same for all the responses so if you can figure out which response works for $t=0$ you have your answer. $\endgroup$ – Farcher Feb 7 '16 at 11:12
  • $\begingroup$ @Farcher Though it is a very good method for objective type question I also want to know the proper method. And I can't calculate q and I at t=0 :( Can you hint at how to do that? And if you know the proper solution please tell me how to go about it. Thanks. $\endgroup$ – Utkarsh Barsaiyan Feb 7 '16 at 11:18
  • $\begingroup$ This is the proper solution in that I would have expected you did not have enough time to do the question from first principles. The instant the switches close the charge is redistributed on the two parallel capacitors so that the voltage across them is the same. $\endgroup$ – Farcher Feb 7 '16 at 11:44