Two identical capacitors are connected in parallel and each acquires a charge Q

Question

Two identical capacitors are connected in parallel and each acquires a charge Q0 when connected to a source of voltage V0. The voltage source is disconnected and then a dielectric (K = 3.1) is inserted to fill the space between the plates of one of the capacitors. Assume that the capacitor without the dielectric is the first and the capacitor with the dielectric is the second.

Part A

Determine the charge now on each capacitor.

Express your answer using two significant figures.

Part B

Express your answer using three significant figures.

Part C

Determine the voltage now across each capacitor.

Express your answer using two significant figures.

Part D

Express your answer using two significant figures.

Explanation / Answer

let capacitor 1 has charge Q0 and potential across it V0

let capacitor 2 has charge Q0 and potential across it V0

when dielectir is inserted in second capacitor it's new capacitance will be C' = 3.1C

a) since they are in parallel they will have same potential V across them

hence

charge on 1st will be same Q1= C*V and charge on second will be Q2 =C2*V = 3.1C*V too.

now the total charge remains conserved that is

Q1+Q2 = 2Q0...............1

and energy remains conserved as well

Q12/C +Q22/3.1C = 2*Qo2/C............2

solving equation we get

Q2 = 1.509 Q0

Q1 = 0.487 Q0

b) V1= Q1/C1 = 0.487 V

V2 = 0.487

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