a 10ufcapacitoris chargedby 30Vd.c supply and then connected across an uncharged
50uf capacitor(1)the final potential difference across the combination (2) the initial and final energies. How will you account for the difference in energy
To find the final potential difference across the combination, we need to apply the principle of conservation of charge.
1) To find the final potential difference across the combination:
- Initially, the 10uF capacitor is charged by a 30V DC supply, so it has a charge Q1 = C1 * V = 10e-6 * 30 = 0.3 mC
- When the 10uF capacitor is connected across the uncharged 50uF capacitor, charge flows from the 10uF to the 50uF capacitor until both have the same potential difference.
- Using the principle of conservation of charge, we know that the total charge remains constant. Therefore, the charge on the 10uF capacitor will transfer to the 50uF capacitor.
- The final charge on the 50uF capacitor will be the sum of the initial charges on both capacitors: Q2 = Q1 = 0.3 mC
- Finally, we can find the final potential difference across the combination by dividing the charge on the 50uF capacitor by its capacitance: V_final = Q2 / C2 = 0.3 mC / 50e-6 = 6V
Therefore, the final potential difference across the combination is 6V.
2) To determine the initial and final energies and account for the difference:
- The initial energy stored in the 10uF capacitor can be calculated using the formula: E_initial = 0.5 * C1 * V^2 = 0.5 * 10e-6 * (30)^2 = 4.5 mJ
- The initial energy stored in the 50uF capacitor is zero since it is uncharged.
- The final energy stored in both capacitors can be calculated using the formula: E_final = 0.5 * C1 * V_final^2 + 0.5 * C2 * V_final^2 = 0.5 * 10e-6 * (6)^2 + 0.5 * 50e-6 * (6)^2 = 0.18 mJ + 0.36 mJ = 0.54 mJ
The difference in energy is accounted for by the transfer of energy from the initially charged 10uF capacitor to the previously uncharged 50uF capacitor. This transfer occurs due to the flow of charge until both capacitors have the same potential difference. Therefore, the difference in energy can be attributed to the redistribution of energy from the initial capacitor to the final combination.