Question

The equivalent capacity of two capacitors in series is 3µF and in parallel is 16µF. Their individual capacities in µF are ______.

Options

• 14, 2

• 12, 4

• 10, 6

• 8, 8

Answer 1

The equivalent capacity of two capacitors in series is 3µF and in parallel is 16µF. Their individual capacities in µF are 12, 4.

Explanation:

For series combination

`"C"_"s" = ("C"_1"C"_2)/("C"_1 + "C"_2)` = 3    ....(1)

C_p = C₁ + C₂ = 16    ....(2)

`therefore ("C"_1"C"_2)/16` = 3

or C₁C₂ = 48    ...(3)

Putting the value of C₁ from equation (2) in Equation (3):

(16 - C₂) C₂ = 48

`16"C"_2 - "C"_2^2 = 48`

or `"C"_2^2 - 16 "C"_2 + 48 = 0`

(C₂ - 12)(C₂ - 4) = 0

∴ C₂ = 12 μF  or  C₂ = 4 μF