GP2 Rec 1 13118 Capacitance and Dielectrics Two identical pa

GP2 Rec. #1, 1/31/18. Capacitance and Dielectrics Two identical parallel plate capacitors are made from 15.0 cm x 15.0 cm parallel plates separated by 1.00 mm with air (dielectric constant K = 1.00, dielectric strength Emax-3.0 MV/m) in the gap. They are connected in series to a battery with an electromotive force (emf) of 125 V through a switch. a) Determine the capacitance C1- C2, and the maximum voltage switch each can withstand before dielectric breakdown of the air. b) Find the amount of charge that flowed through the switch when it was closed c) Now the switch is opened. Then a piece of Pyrex glass (dielectric constant 5.66, dielectric strength ERAX 14 MV/m) is inserted into the gap in C2, without disturbing the charges. What does the voltage on C2 become? d) (optional) With the Pyrex still inside C2, the switch is closed. What is the final charge on C2?

Solution

(A) C = C1 = C2 = e0 K A / d

= (8.854 x 10^-12 x 1 x 0.15^2) / (1 x 10^-3)

= 1.992 x 10^-10 F

V = E d = (3 x 10^6 V/m) (1 x 10^-3 m)

V = 3000 Volt

(B) 1/Ceq = 1/C1 + 1/C2

CEq = C/2 = 9.96 x 10^-11 F

Q = Ceq V =12.45 x 10^-9 C

(C) C2\' = k C2 = 5.60 x 1.992 x 10^-10 = 1.115 x 10^-9 F

V = Q / C2\' = 11.2 Volt

(D) Ceq = (11.15 + 1.992)/(11.15 x 1.992) x 10^-10

= 0.592 x 10^-10 F

Q = Ceq V = 7.10 x 10^-9 C