Question

three capacitor of equal capacity c are joined first in parallel and then in series the ratio of equivalent capacitance will be​

Answer 1

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Answer 2

Given: Three capacitors of equal capacity - C₁, C₂, and C₃ = C

            Equivalent capacitance in series = Cₐ

            Equivalent capacitance in parallel = Cₓ

To Find: Ratio of equivalent capacitance, R = Cₓ/Cₐ

Solution:

To calculate R, the formula used:

• Equivalent capacitance in parallel, Cₓ = C₁ + C₂ + C₃ ........+ Cₙ
• Equivalent capacitance in series, Cₐ = 1/C₁ + 1/ C₂+ 1/C₃........+ 1/Cₙ

Applying the above formula :

For Cₓ i.e. in parallel connection-

Cₓ = C₁ + C₂ + C₃

    = C +C +C

    = 3C

Cₓ = 3C                                       ⇒ 1

For Cₐ  i.e. in series connection-

1/Cₐ  = 1/C₁ + 1/ C₂+ 1/C₃

     = 1/C +1/C + 1/C

     = 3 / C

1/Cₐ  = 3/C

Reciprocal on both sides:

Cₐ   = C /3                                   ⇒ 2

On dividing equations 1 and 2 :

Cₓ / Cₐ = 3C / ( C/3)

           = 3x3xC / C

           = 9 C / C

          = 9 /1

Cₓ / Cₐ = 9 / 1

R = 9 /1

Hence, the ratio of equivalent capacitance in parallel and series connections is 9 / 1 .