# Two Capacitors One Resistor [closed]

The initial charge of the capacitor C1 is $$q_0$$ and capacitance is $$C_1$$ and capacitor C2 is $$0$$ and capacitance is $$C_2$$. When the switch S is closed the first capacitor charges the second one and during that process some energy has been dissipated in the resistor, thus transferred to heat. Find how much energy is lost to heat? The answer must be in terms of given quantities, which means that I am looking for a formula rather than a numberic answer.

In order to solve this problem, I thought that it will be beneficial to find $$I(t)$$ and then find the power in the equation $$P = I(t)^2 R$$. After finding the power, I thought that it is a good idea to integrate from the boundries 0 to infinity. However, I was not able to find the $$I(t)$$ since there are two capacitors with a different capacitance.

## closed as off-topic by John Rennie, GiorgioP, Jon Custer, FGSUZ, ZeroTheHeroMar 31 at 12:52

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• What are the values (capacitances) of the capacitors? – Bob D Mar 26 at 19:00
• Capacitor C1 has the capacitance $C_1$ and Capacitor C2 has the capacitance $C_2$ – Demir Eken Mar 26 at 19:01
• What are the values, how many Farads or microfarads of capacitance for C1 and C2? – Bob D Mar 26 at 19:08
• Sir, I want to find an answer in terms of $C_1$ and $C_2$ but not microfarads. This is a more theoric question rather than a numeric question, so I need to find the answer in terms of given quantities. – Demir Eken Mar 26 at 19:10
• OK, you should have said that you were looking for a formula for the amount of energy in Joules. The question sounded like you were looking for a number. Suggest you edit the question to say that. – Bob D Mar 26 at 19:14

We are not supposed to answer homework and exercise questions, but here is some guidance. The key point is that both energy and charge are conserved and the final voltage on each capacitor will be the same. Try the following steps.

1. Write the formula for the initial energy stored in capacitor $$C_{1}$$.

2. Write down the relationship between voltage, charge and capacitance. Express the initial voltage $$V_{1}$$ on $$C_{1}$$ in terms of the charge $$q_{0}$$ and capacitance $$C_{1}$$

3. You don't know what the final charge will be on each capacitor, but you do know that the sum of the charges must equal $$q_{0}$$ for conservation of charge.

4. You also know that at the end the current will be zero and the voltages on the two capacitors will then have to be the same.

5. With the equations developed so far, you should be able to express the final voltages on the two capacitors in terms of $$C_{1}$$, $$C_{2}$$ and $$q_{0}$$.

6. Then you can express the final STORED energy in the each of the two capacitors in terms of $$C_{1}$$, $$C_{2}$$ and $$q_{0}$$. Add them for the final STORED energy in the circuit.

7. Finally, you know that the energy dissipated in the resistor will equal the initial stored energy (step 1 above) minus the final stored energy (step 6) for conservation of energy.

Notice that the value of the resistance R is irrelevant in solving the problem.

Hope this helps

• In my opinion, this is too much detail for a homework-like question. (Perhaps edit it down to give gentle guidance rather than a recipe?) – garyp Mar 26 at 20:14
• @garyp OK. I'll make it bare bones to start. – Bob D Mar 26 at 20:15
• @garyp I couldn't edit it fast enough before it was accepted. But thanks for the advice for future reference. Bob – Bob D Mar 26 at 20:18
• @garyp At least I didn't give all the formulas! – Bob D Mar 26 at 20:19
• Thank you very much for your help, this answer provided me a really good guide based on how I should think. – Demir Eken Mar 26 at 20:20