When a capacitor is charged, it stores energy in the form of an electric field. The charge on a capacitor is given by the formula:

Q = CV

where Q is the charge on the capacitor, C is the capacitance, and V is the voltage across the capacitor.


The energy stored in a capacitor is given by the formula:

E = 1/2 CV^2

where E is the energy stored, C is the capacitance, and V is the voltage across the capacitor.


When a charged capacitor is connected to another uncharged capacitor in parallel, the charge on the first capacitor distributes equally between the two capacitors. This is because the voltage across both capacitors is the same, and the capacitance of both capacitors is the same.


The initial energy stored in the capacitor is given by:

E1 = 1/2 (0.1) (10)^2 = 5 J

When the charged capacitor is connected to the uncharged capacitor, the charge on the first capacitor distributes equally between the two capacitors. The total capacitance of the two capacitors connected in parallel is:

C = C1 + C2 = 0.1 + 0.1 = 0.2 F

The voltage across both capacitors is the same and is given by:

V = Q/C

where Q is the charge on the capacitor. Since the charge is distributed equally between the two capacitors, the charge on each capacitor is:

Q/2

Therefore, the voltage across each capacitor is:

V = (Q/2)/C = Q/2C

The final energy stored in each capacitor is given by:

E2 = 1/2 C (Q/2C)^2 = 1/8 Q^2/C

The total final energy stored in both capacitors is:

E_total = 2E2 = Q^2/C

The charge on the capacitor is given by:

Q = CV

where V is the voltage across the capacitors. Since the voltage across both capacitors is the same, we have:

Q = C(V1 + V2)

where V1 and V2 are the voltages across the two capacitors. Since the charge on the capacitor is distributed equally between the two capacitors, we have:

Q/2 = C(V1 + V2)/2

Therefore, the voltage across each capacitor is:

V1 = V2 = Q/2C

Substituting this into the expression for the final energy stored, we get:

E_total = Q^2/C = (2CV1)^2/C = 4V1^2C

The ratio of final energy stored to initial energy stored is therefore:

E_total/E1 = (4V1^2C)/5 = (4(Q/2C)^2C)/5 = Q^2/10

Substituting Q = CV, we get:

E_total/E1 = (CV)^2/10 = V^2C/10

The voltage across the capacitors is given by:

V = Q/C = 2CV1/C = 2V1

Therefore, we have:

E