# Capacitor problem - Calculate the heat in connecting wires

1. Apr 18, 2014

### LHC_23

Capacitor problem -- Calculate the heat in connecting wires

1. The problem statement, all variables and given/known data
A $5.0$$\mu$$F$ capacitor is charged to $12 V$ . The positive plate of this capacitor is now connected to the negative terminal of a $12 V$ battery and vice versa. Calculate the heat developed in the connecting wires.

2. Relevant equations
$W = QV$

$E = 0.5CV^2$

3. The attempt at a solution

I know from the above 2 equations that half of the energy supplied by the battery should be lost as heat . But I don't know how to proceed with this problem ?

2. Apr 18, 2014

### rude man

That statement is incorrect since there is an initial charge on the capacitor.
In this particular case, what is the capacitor stored energy before (t<0) and after (t=∞)? Which says what about the fraction of battery energy lost to heat?

So, back to fundamentals:

You need to write the KVL around the loop including consideration of the initial voltage on C.
This starts as an integral equation in current i but you can make it a 1st order differential equation in i with the appropriate initial condition, getting you i(t), then integrate R∫(i^2)dt from 0 to infinity for the total power dissipation where R is the wire resistance.

There may be a shortcut here using only initial and final capacitor stored energy but I don't see one.

3. Apr 18, 2014

### Tanya Sharma

Hello rude man...

Do you get 2CE2 as the heat dissipated as well as the work done by battery ? Here C is the capacitance and E is the EMF of the battery .

4. Apr 18, 2014

### ehild

It is right.

ehild

5. Apr 18, 2014

### rude man

Yes I do Tanya.