Introduction:
When two capacitors are connected in parallel, the total capacitance increases and the voltage across each capacitor becomes the same. In this scenario, capacitor c1 (2mf) is charged to a voltage of 100 V and capacitor c2 (4mf) is charged to a voltage of 50 V.

Calculation of total capacitance:
When capacitors are connected in parallel, the total capacitance is given by the formula:

C(total) = C1 + C2

C(total) = 2mf + 4mf

C(total) = 6mf

Therefore, the total capacitance when the two capacitors are connected in parallel is 6mf.

Calculation of total charge:
The total charge on the capacitors before they are connected in parallel is given by the formula:

Q(total) = C1 x V1 + C2 x V2

Q(total) = 2mf x 100V + 4mf x 50V

Q(total) = 200mfV + 200mfV

Q(total) = 400mfV

Therefore, the total charge on the capacitors before they are connected in parallel is 400mfV.

Calculation of final voltage:
When the capacitors are connected in parallel, the voltage across each capacitor becomes the same. Therefore, the final voltage across each capacitor is given by the formula:

V(final) = Q(total) / C(total)

V(final) = 400mfV / 6mf

V(final) = 66.67V

Therefore, the final voltage across each capacitor when they are connected in parallel is 66.67V.

Calculation of energy loss:
The energy loss in the parallel connection of capacitors is given by the formula:

E(loss) = (C1 x V1^2 + C2 x V2^2 - C(total) x V(final)^2) / 2

E(loss) = (2mf x 100V^2 + 4mf x 50V^2 - 6mf x 66.67V^2) / 2

E(loss) = (20,000mfV^2 + 10,000mfV^2 - 22,225mfV^2) / 2

E(loss) = 7,887.5mJ

Therefore, the energy loss in the parallel connection of capacitors is 7,887.5mJ.

Explanation of energy loss:
The energy loss occurs due to the conversion of electrical energy into heat energy during the charging and discharging of the capacitors. When the capacitors are charged to different voltages and then connected in parallel, the charge flows from the capacitor with higher voltage to the capacitor with lower voltage until the voltages across both capacitors become equal. During this process, energy is lost due to the internal resistance of the capacitors and the wires connecting them. This energy loss is dissipated as heat energy and cannot be recovered. Therefore, the energy loss in the parallel connection of capacitors is an important consideration in practical applications.