What Potential Difference Is Needed for Series Capacitors to Store Same Energy?

[nate559]

Two capacitors, C1 = 20 µF and C2 = 5.0 µF, are connected in parallel and charged with a 150 V power supply

A.) Energy Stored I found to be is 2.81*10^-1 J

B.)What potential difference would be required across the same two capacitors connected in series in order that the combination store the same energy as in (a)?

Delta V= sqrt of (2*Energy stored/C) This eqn can b used to solve for delta V

I have no idea what I am doing wrong! I have used the capacitor in parallel combo of C= C1+C2... Then I have converted the microFaraday charges of these sums to Faraday but no success

Any Suggestions??

 

[Kurdt]

You know that the effective capacitance of capacitors in series is given by:

$$\frac{1}{C}=\frac{1}{C_1} + \frac{1}{C_2}...$$

You also know that the energy stored is given by:

$$E=\frac{1}{2}CV^2$$

So you have rearranged perfectly well but the problem could just be that you are using the parallel combination rather than the series combination to find the effective capacitance.

 

[m2003]

I would first check the calculations to ensure they were done correctly. It is important to use consistent units when performing calculations involving different quantities. In this case, it appears that the units for the capacitance values were not converted to Farads before calculating the energy stored. Additionally, it is important to use the correct formula for calculating the energy stored in a capacitor, which is E = 1/2 * C * V^2.

Once the calculations have been checked and corrected, the next step would be to answer the second question about the potential difference required for the capacitors in series. As mentioned in the question, the formula to use would be Delta V = sqrt(2 * E / C). Again, it is important to use consistent units and to plug in the correct values for energy and capacitance. This will give the potential difference required for the capacitors in series to store the same amount of energy as in part (a).

If the calculations still do not match, it may be helpful to double check the values for the capacitance and potential difference given in the problem statement to ensure they were copied correctly. It may also be helpful to seek assistance from a colleague or reference a reliable source for the correct formulas and equations for calculating energy stored in capacitors.