Charging capacitor by another capacitor

[bgq]

Hi,

Consider a charged capacitor connected to a an empty capacitor. The charged capacitor starts to discharge while the empty capacitor starts charging. The whole process finishes when the two capacitors maintain the same potential difference. The problem is that when calculating the energies at the beginning and at the end, we find that they are different. Some books says that the lost energy is dissipated in the connecting wires, yet others say that the energy is transformed into electromagnetic waves.

How can we interpret the loss of the electric energy in this case?

 

[Philip Wood]

Both types of energy transfer will take place, but which one dominates will depend on the details of the system such as the resistance and inductance of the wires used to join the capacitors.

 

[tiny-tim]

hi bgq!

the energy loss equals I²R, so it's certainly the loss through the resistor

from the pf library on capacitor …


Inverse exponential rate of charging:

A capacitor does not charge or discharge instantly.

When a steady voltage $V_1$ is first applied, through a circuit of resistance $R$, to a capacitor across which there is already a voltage $V_0$, both the charging current $I$ in the circuit and the voltage difference $V_1\,-\,V$ change exponentially, with a parameter $-1/CR$:

$$I(t) = \frac{V_1\,-\,V_0}{R}\,e^{-\frac{1}{CR}\,t}$$

$$V_1\ -\ V(t) = (V_1\,-\,V_0)\,e^{-\frac{1}{CR}\,t}$$

So the current becomes effectively zero, and the voltage across the capacitor becomes effectively $V_1$, after a time proportional to $CR$.

Energy loss:

Energy lost (to heat in the resistor):

$$\int\,I^2(t)\,R\,dt\ =\ \frac{1}{2}\,C (V_1\,-\,V_0)^2$$

 

[bgq]

Thank you very much

 

[sardar]

I would approach this scenario by first considering the principles of conservation of energy and charge. In this situation, we have two capacitors that are connected in a circuit, and the total charge and energy in the system should remain constant throughout the process. Therefore, any discrepancy in energy calculations should be accounted for by the transfer of energy between the capacitors and the surrounding environment.

One possible explanation for the difference in energy calculations could be the presence of resistive elements in the connecting wires. As the charged capacitor discharges and the empty capacitor charges, there will be a flow of current through the wires, and this current will experience some resistance. This resistance leads to the dissipation of energy in the form of heat, which could account for the discrepancy in energy calculations.

Another explanation could be the emission of electromagnetic waves during the charging and discharging process. As the charges move back and forth between the two capacitors, they can create electromagnetic waves that carry energy away from the system. This energy loss would also need to be taken into account when calculating the final energy of the system.

Ultimately, the exact cause of the energy loss in this scenario may depend on the specific parameters of the capacitors and the circuit. It is important to carefully consider all potential factors, such as resistive elements and electromagnetic waves, in order to accurately interpret the loss of electric energy in this case.