Question

The combined capacity of a parallel combination of two capacitors is 4 times their combinrd capacity when connected in series. this happens if their capacities are

Answer 1

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Let the capacitances be C₁ and C₂

Effective capacitance in :

Series = C₁C₂/(C₁ + C₂)

Parallel = C₁ + C₂

By the given conditions,

C₁ + C₂ = 4C₁C₂/(C₁ + C₂)

(C₁ + C₂)(C₁ + C₂) = 4C₁C₂

C₁² + C₂² + 2C₁C₂ = 4C₁C₂

C₁² + C₂² - 2C₁C₂ = 0

(C₁ - C₂)² = 0

C₁ - C₂ = 0

C₁ = C₂

Hence the given conditions occur only if both the capacitances are equal