Consider two parallel-plate capacitors, C 1 and C 2 , that are connected in para

Question

Consider two parallel-plate capacitors, C1 and C2, that are connected in parallel. The capacitors are identical except that C2 has a dielectric inserted between its plates. A210 V battery is connected across the combination until electrostatic equilibrium is established, and then the battery is disconnected.

(a) What is the charge on each capacitor? (Use the following as necessary: C1 and ?. Do not include the unit for the voltage in your answers.)

(b) What is the total stored energy of the capacitors? (Use the following as necessary: C1 and ?. Do not include the unit for the voltage in your answers.)
U =  

(c) The dielectric is removed from C2. What is the final stored energy of the capacitors? (Use the following as necessary: C1 and ?. Do not include the unit for the voltage in your answers.)
Uf =  

(d) What is the final voltage across the two capacitors? (Use the following as necessary: C1 and ?. Do not include the unit for the voltage in your answers.)
Vf =

Explanation / Answer

Assuming C1 = 1 pF, C2=3C1 = 3 pF

a.) Q1 = C1*V = 2.1 x 10^-10 C

Q2 = C2*V = 6.3 x 10^-10 C

b.)U = 0.5*Q1*V + 0.5*Q2*V = 8.82 x 10^-8 J

c.) Q1new = Q2new = (Q1+Q2)/2 = 4.2 x 10^-10 C

U = Q1new^2/2C1 + Q2new^2/2C2 = 11.76 x 10^-8 J

d.) V1new = V2new = Q1new/C1 = 420 V

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