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Q.

The equivalent capacitance of three capacitors of capacitance C₁, C₂ and C₃ are connected in parallel is 12 units and product C₁.C₂.C₃ = 48. When the capacitors C₁ and C₂ are connected in parallel, the equivalent capacitance is 6 units. Then the capacitance are

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a

1.5, 2.5, 8

b

1, 5, 6

c

2, 3, 7

d

4, 2, 6

answer is D.

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Detailed Solution

C₁ + C₂ + C₃ = 12..(i)

C₁C₂C₃ = 48….(ii)

C₁ + C₂ = 6……(iii)

From equations (i) and (iii) C₃ = 6…(iv)

From equations (ii) and (iv) C₁C₂= 8

Also (C₁ – C₂)² = (C₁ + C₂)² – 4C₁C₂ $\Rightarrow$ (C₁ – C₂)² = (6)² – 4 × 8 = 4 $\Rightarrow$ C₁ – C₂ = 2…(v)

On solving (iii) and (v) C₁ = 4, C₂ = 2.

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The equivalent capacitance of three capacitors of capacitance C1, C2 and C3 are connected in parallel is 12 units and product C1.C2.C3 = 48. When the capacitors C1 and C2 are connected in parallel, the equivalent capacitance is 6 units. Then the capacitance are