Two capacitors are connected in parallel and connected to a 6V battery. Each cap

Question

Two capacitors are connected in parallel and connected to a 6V battery. Each capacitor has a plate area of 1 cm^2 and a plate separation of 1mm. They initially have a vacuum between the plates. 1) Calculate the capacitance of one of the capacitors and the total capacitance for the pair of capacitors. 2) Calculate the charge on each capacitor. 3) The capacitors are now disconnected from the battery (when fully charged) and a 1 mm sheet of mylar (dielectric constant k = 3.30) is slipped between the plates of one of them. Calculate the new capacitance and the new voltage across the capacitor with mylar. 4) If the capacitors are now reconnected in parallel, determine the charge on each and the potential difference across them. Start from conservation laws and what must be the same for both capacitors when connected as shown.

Explanation / Answer

1) Here ,

for the capcitance of each capcitor

C = A * epsilon/d

C = 8.854 *10^-12 * 1 *10^-4/(0.001)

C = 8.854 *10^-13 F

for the net capacitance in parallel

Cnet = 2 * C = 1.771 *10^-12 F

b)

charge on each capacitor = C * V

charge on each capacitor = 8.854 *10^-13 * 6

charge on each capacitor = 5.31 *10^-12 C

c)

d' = 1 mm

k = 3.3

for the new capacitance

Cnew = k * C

Cnew = 3.3 * 8.854 *10^-13 F

Cnew = 2.92 *10^-12 F

the new capacitance is 2.92 *10^-12 F

new voltage = 6/3.3

new voltage = 1.82

4)

Now, when they are connected

let the charge flown from the capacitor is q

then for the same potential across both

(5.31 *10^-12 - q)/(8.854 *10^-13) = (5.31 *10^-12 + q)/2.92 *10^-12

solving for q

q = 2.83 *10^-12 F

charge on the capacitor without dielectric = 5.31 *10^-12 - 2.83 *10^-12

charge on the capacitor without dielectric = 2.48 *10^-12 F

-------------

charge on the capcitor with dielectric = 5.31 *10^-12 + 2.83 *10^-12

charge on the capcitor with dielectric = 8.14 *10^-12 F
--------------------------

potential across the capacitor = 2.48 *10^-12/(8.854 *10^-13)

potential across the capacitor = 2.81 V

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