RC circuit switching at t=0 from A to B

[paddu123]

For the attached rc circuit, at time 0, the switch switches from A to B, how to figure out the voltage wave form at B?

When switch switches from A to B, charge has to redistribute between capacitors, but as the voltage across capacitor C2 can't change instantaneously initially there is a spark and charge distributes slowly. Please help me if this is right to interpret or not?

 

[ehild]

I do not see any R. Where is it? ehild

 

[paddu123]

Hi ehild,
Yes. No R in the circuit. Just named it as rc circuit. Sorry for the naming convention confusion.

Thanks,
paddu

 

[Antiphon]

There are no sparks in circuit theory.

There will be an infinitely short time of infinite current and voltage will instantaneously change.

 

[rude man]

You've opened up a can of worms! You're going to hear all kinds of loopy explanations probably, including my favorite which is that electromagnetic radiation takes place.

First, if you saw a spark it must have been due to the large inrush current from C1 to C2. As the connection is made, impedance Z changes in finite time from ∞ to 0. So i²Z can be pretty large for a very short time, even causing visible heating, e.g. sparks.

But the real issue is not that: let's say both C1 and C2 are equal in value: C1 = C2 = C. So that initially C1 is charged up to Q1 = C*V, while Q2 = 0. Then, so that charge is conserved, Q1' + Q2' = Q1. OK, so Q1' = Q2' = Q1/2 and V' = V/2. All OK so far.

But then some weisenheimer notices that the energy stored in C1 and C2 is less after the switch than before: energy before = (1/2)CV², energy after =
(1/2)C(V/2)² + (1/2)C(V/2)² = (1/4)CV²! Oops, where did the other half of the energy go?

I'll leave it there for you to contemplate asnd read all the pings you get. I'll rejoin the fray later one way or another.

 

[Antiphon]

Rude man has brought up lots of fun questions. Before the thread itself gets short circuited, insert a resistor R in series with the switch and solve the equations using R. Then allow R->0. This will take you to the correct answer in the same way as finding the limit of x/x as x->0.

If you want to blow the instructor's mind, answer Rude man's riddle about where the energy went using the equations you derive. I promise you'll get a good grade in the class.