[SOLVED] What is the response of the given circuit

[iVenky]

There are two capacitors C1 (4 F) and C2 (16 F). They are separated by a switch. The switch closes at t=0.
When t<0 the voltage in C1 is 10V. What will happen when the switch is closed? What will be the voltage across C1 and C2 now (ie t>0) ?

Thanks in advance.

 

[erikl]

There are two capacitors C1 (4 F) and C2 (16 F). They are separated by a switch. The switch closes at t=0.
When t<0 the voltage in C1 is 10V. What will happen when the switch is closed?

160 J of energy will be dissipated into heat and/or electromagnetic (radio) energy.

 

[iVenky]

160 J of energy will be dissipated into heat and/or electromagnetic (radio) energy.

I mean what will be the voltage across C1 and C2?

 

[erikl]

I mean what will be the voltage across C1 and C2?

2V , of course.

 

[iVenky]

I tried that using Pspice and I am getting 10 V.

I have attached the image.

 

[FvM]

Unfortunately, your schematic is different from your previous description.

The original question (shorting a switch beteen two capacitors) involves infinite currents and an insolvable differential equation when assuming ideal components. Doesn't sound like a well considered text book exercise or homework problem.

 

[BradtheRad]

There's an irresistible logic to thinking in terms of 10V on a 4F cap as being a certain number of units of energy.

Then this energy is divided among 20F.

Intuitively it seems as though the answer should be 2V.

My simulator confirms this is the case.

 

[albbg]

If you consider two capacitors C1 and C2 in parallel, separated by a switch, where C1 is charged at Vi volts, and C2 is not charged then:

Charge in C1: q1 = C1*Vi Coulombs
Charge in C1: q2 = 0 Coulombs

When the switch is closed the totale charge (q1+q2) must be conserved because there is no way to make it flows outside the circuit since it is insulated, then (if Vo is the final voltage across the two capacitors):

C1*vi + 0 = C1*Vo + C2*Vo

then:

Vo = C1/(C1+C2)*Vi

If C1=4F, C2=16F and Vi=10V:

Vo = 4/(16+4)*10 = 2V

You can note that the initial energy of the system was:

Ei = 0.5*C1*Vi^2 = 0.5*4*100 = 200 joule

but the final energy is only:

Ef = 0.5*C1*Vo^2 + 0.5*C2*Vo^2 = 0.5*4*4 + 0.5*16*4 = 40 joule

To balance the 200 - 40 = 160 joule, a spike (dirac pulse) will be generated when the switch is closed.

 

[RobG]

Unfortunately, your schematic is different from your previous description.

The original question (shorting a switch beteen two capacitors) involves infinite currents and an insolvable differential equation when assuming ideal components. Doesn't sound like a well considered text book exercise or homework problem.

You can actually do this problem... assume a finite switch resistance and solve the problem. You'll find that the answer does not depend on resistance. You can also do it using charge conservation: Total charge before = total charge after (like I see albbg did).

 

[iVenky]

If you consider two capacitors C1 and C2 in parallel, separated by a switch, where C1 is charged at Vi volts, and C2 is not charged then:

Charge in C1: q1 = C1*Vi Coulombs
Charge in C1: q2 = 0 Coulombs

When the switch is closed the totale charge (q1+q2) must be conserved because there is no way to make it flows outside the circuit since it is insulated, then (if Vo is the final voltage across the two capacitors):

C1*vi + 0 = C1*Vo + C2*Vo

then:

Vo = C1/(C1+C2)*Vi

If C1=4F, C2=16F and Vi=10V:

Vo = 4/(16+4)*10 = 2V

You can note that the initial energy of the system was:

Ei = 0.5*C1*Vi^2 = 0.5*4*100 = 200 joule

but the final energy is only:

Ef = 0.5*C1*Vo^2 + 0.5*C2*Vo^2 = 0.5*4*4 + 0.5*16*4 = 40 joule

To balance the 200 - 40 = 160 joule, a spike (dirac pulse) will be generated when the switch is closed.

Hello I understood about the charge conservation. But I couldn't understand that spike. What's that spike? (I know little about this switch thing.)

---------- Post added at 19:07 ---------- Previous post was at 19:04 ----------

How to do this in Pspice. I had attached the image in one of my previous posts and I think that there's something wrong in the schematic. I would be much obliged if you could say where the mistake is?

 

[FvM]

How to do this in Pspice. I had attached the image in one of my previous posts and I think that there's something wrong in the schematic. I would be much obliged if you could say where the mistake is?

SPICE doesn't know negative times or +0 and -0. It recognizes both switches closed during initial solution, resulting in balanced charges. You should close the switch at a time t1>0, not t=0.

But I couldn't understand that spike. What's that spike?

To turn the circuit in a real world one with finite currents, the switch must have a series resistance. The PSpice switch component already has, otherwise it would generate a simulation error.

 

[iVenky]

SPICE doesn't know negative times or +0 and -0. It recognizes both switches closed during initial solution, resulting in balanced charges. You should close the switch at a time t1>0, not t=0.

How to change the time? Please help me.

Thanks in advance.

 

[FvM]

How to change the time?

Are you joking? How about tclose = 1u?

You need to perform a transient analysis, by the way.

 

[iVenky]

Are you joking? How about tclose = 1u?

You need to perform a transient analysis, by the way.

I know transient analysis. I don't know how to do that in pspice. I will try what you have said.

 

[iVenky]

I know transient analysis. I don't know how to do that in pspice. I will try what you have said.

I tried what you have said but I didn't get it.

I would be much obliged if you help me.

Thankzzzzzzzz

 

[FvM]

O.K., I have forgotten something. The PSpice switch has a leakage resistance, you can see it in the device parameters. You need a shorting switch across the first capacitor or a similar means, e.g an initial condition statement to keep the capacitor discharged.

 

[iVenky]

I still don't get it.

Please help me.

 

[FvM]

You'll need to connect the shorting switch in parallel to C1.

 

[iVenky]

Hello FvM



Still I didn't get. Please don't give up. I rely on you

Thanks

 

[iVenky]

If you have done this using Pspice you can upload the image.

Thanks