- #1
Robert S
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The following circuit is given:
[PLAIN]http://img822.imageshack.us/img822/6369/image2lz.jpg
Switch S is closed until the charge q2 on C2 reaches its maximum, then at t=0 the switch is opened. Find q1(t).
Using Kirchkoff's rules I found:
EMF= (q1)/(C1+I2R
I2R= q2/C2
I1= I2+I3
In order to solve for q1 I need to substitute [itex]I_1=\frac{dq_1}{dt}[/itex] and solve the differential equation. But I need one more equation to eliminate I3 and q2.
I was thinking of relating the charge q2 to the total charge in the circuit, but after some calculation I found that the total charge isn't constant.
At t=0 the total charge q2 on C2 is EMF*C2 and the charge on C1 is zero.
At t=[itex]\inf[/itex] the total charge on both capacitors is [itex]EMFC_1C_2 / (C_1 + C_2)[/itex] (since the current is zero you can combine the two capacitors using [itex] C_3^{-1}=C_1^{-1} + C_2^{-1}[/itex])
any help is appreciated :-)
edit: I tried to put the kirchkoff equations in Latex, but for some reason the rest of the post becomes unreadable.
[PLAIN]http://img822.imageshack.us/img822/6369/image2lz.jpg
Switch S is closed until the charge q2 on C2 reaches its maximum, then at t=0 the switch is opened. Find q1(t).
Using Kirchkoff's rules I found:
EMF= (q1)/(C1+I2R
I2R= q2/C2
I1= I2+I3
In order to solve for q1 I need to substitute [itex]I_1=\frac{dq_1}{dt}[/itex] and solve the differential equation. But I need one more equation to eliminate I3 and q2.
I was thinking of relating the charge q2 to the total charge in the circuit, but after some calculation I found that the total charge isn't constant.
At t=0 the total charge q2 on C2 is EMF*C2 and the charge on C1 is zero.
At t=[itex]\inf[/itex] the total charge on both capacitors is [itex]EMFC_1C_2 / (C_1 + C_2)[/itex] (since the current is zero you can combine the two capacitors using [itex] C_3^{-1}=C_1^{-1} + C_2^{-1}[/itex])
any help is appreciated :-)
edit: I tried to put the kirchkoff equations in Latex, but for some reason the rest of the post becomes unreadable.
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