Question

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

Answer 1

Answer:

0.75F

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;

$\frac{1}{C}$ = $\frac{1}{C_1}$ + $\frac{1}{C_2}$ + $\frac{1}{C_3}$  -------------------(i)

Now to solve the question,

Let;

C₁ = 1.0F

C₂ = 5.0F

C₃ = 8.0F

Substitute these values into equation (i) as follows;

$\frac{1}{C}$ = $\frac{1}{1.0}$ + $\frac{1}{5.0}$ + $\frac{1}{8.0}$

Solve for C

$\frac{1}{C}$ = $\frac{40.0 + 8.0 + 5.0}{40.0}$

$\frac{1}{C}$ = $\frac{53.0}{40.0}$

C = $\frac{40.0}{53.0}$

C = 0.75

Therefore, their total capacitance is 0.75F