Energy Loss in Capacitors: How Can We Account for It?

[SpartanG345]

Homework Statement

PART D

this is an example from my textbook, i do not understand the result however

Homework Equations

U = W = Q^2/(2v) = 0.5 CV^2 = 0.5 QV

the charge once connected
Q1 640 micro F
Q2 320 micro F

V1=V2 = 80V (equating the charges to total Q0 initially stored in the capacitor)

The Attempt at a Solution

part d asks to find the total energy in the system, however in the answers
the book found the total energy in the system to be

0.038J ( once both capacitors are connected)

however the energy required to charge up the first capacitor is 0.058J - i thought this should be the total energy of the system.

this does not make sense, how can there be energy loss, as the formula didn't take account of energy loss. The book found the energy in the system by working out the charge in each capacitor the working out the total energy using equation 2

i just can't see how method took account of energy loss, using formulas to my understanding that did not consider energy loss.

 

[Dadface]

When the capacitors are joined current flows through the connecting wires which heat up as a result.This is the major source of energy loss.There may also be small losses due to inductive effects and any sparks that may be produced.

 

[SpartanG345]

 

[SpartanG345]

wat i don't get is how the formulas that didn't account of energy loss show that there is energy loss, this seems impossible.

 

[willem2]

wat i don't get is how the formulas that didn't account of energy loss show that there is energy loss, this seems impossible.

I don't see what the problem is. If I use conservation of momentum to find out the result of an inelastic collision, I don't take account of the energy. If I calculate the kinetic energy after the collison, it will show a loss.

 

[berkeman]

wat i don't get is how the formulas that didn't account of energy loss show that there is energy loss, this seems impossible.

The best way to understand this is to insert a real resistor between the capacitors, and calculate the energy dissipated in the resistor. Then cut the value of the resistor in half, and re-do the calculation. Do you see a pattern?

 

[SpartanG345]

After fiddling around

i found the % energy loss when one capacitor discharges into another

is C1/(C1 + C2)

eg if the capacitors were the same then the energy loss is 50%, this doesn't really make sense as there is no R, which means the only way the energy could have been lost is due to EMR, but i need to revise that topic for my Phys exam in 3 days

 

[berkeman]

After fiddling around

i found the % energy loss when one capacitor discharges into another

is C1/(C1 + C2)

eg if the capacitors were the same then the energy loss is 50%, this doesn't really make sense as there is no R, which means the only way the energy could have been lost is due to EMR, but i need to revise that topic for my Phys exam in 3 days

R is not zero. Did you do the calculations that I described in my previous post?