Question

Find the ratio of potential differences that must be applied across the parallel and series combination of two capacitors C1 and C2with their capacitance in the ratio 1:2 so that the energy stored in the two cases becomes the sane plot the graph between energy and capacitance

Answer 1

C2 = 2 C1.

parallel combination:   C_eq = 3 C1
       Energy  E = 1/2 * C_eq * V1² = 3/2 * C1 V1²

Series combination:   C_eq = C1 C2 /(C1 +C2) = 2 C1/ 3
       Energy E = 1/2 * 2/3 * C1 * V2² = 1/3 * C1 V2²

Equating energies, we get   V1 : V2 = √2 : 3

Plot of energy vs Capacitance:
    This will be linear  if Voltage applied is assumed to be constant.

Answer 2

Answer:

ANSWER is 1/2

Explanation:

GIVEN:-    C1/C2 =1/2

                  Cp=C1+C2

                  Cs=1/C1+1/C2

ENERGY IS GIVEN BY:-

                   Ep=1/2CpV1^2

                   Es=1/2CsV2^2

                     

                   Ep=Es  (given)

so,              1/2CpV1^2=1/2CsV2^2

                   Cp/Cs=(V2/V1)^2

                   Cs/Cp=(V1/V2)^2

                    (V1/V2)^2=C1C2/C1+C2/C1+C2

By solving these we get

                     (V1/V2)^2= C1/C2/[C1/C2+1]

                                      =ROOT1/4

                                      =1/2         =}  PROVED