Question

Find the total capacitance for three capacitors connected in series, given their individual

capacitances are 1.0 F, 5.0 F, and 8.0 F.

Answer 1

0.75F

Step-by-step explanation:

When capacitors are connected in series, the reciprocal of their total capacitance is the sum of the reciprocals of their individual capacitances. In other words, when, say, three capacitors, C₁, C₂ and C₃ are connected in series, their total capacitance, C, is given by;

`(1)/(C)` =
`(1)/(C_1)` +
`(1)/(C_2)` +
`(1)/(C_3)` -------------------(i)

Now to solve the question,

Let;

C₁ = 1.0F

C₂ = 5.0F

C₃ = 8.0F

Substitute these values into equation (i) as follows;

`(1)/(C)` =
`(1)/(1.0)` +
`(1)/(5.0)` +
`(1)/(8.0)`

Solve for C

`(1)/(C)` =
`(40.0 + 8.0 + 5.0)/(40.0)`

`(1)/(C)` =
`(53.0)/(40.0)`

C =
`(40.0)/(53.0)`

C = 0.75

Therefore, their total capacitance is 0.75F