Question

A $6mF$capacitor, a $10mF$capacitor, and a $16mF$capacitor are connected in series. What is their equivalent capacitance?

Short answer

The capacitance is$3\mu F$.

Step-by-step solution

Given information

We have given that $A6mF$capacitor, a $10mF$capacitor, and a $16mF$capacitor are connected in series.

We need to find that their equivalent capacitance.

Simplify

Let $C_1=6muf$,$C_2=16\mu F$, and $C_3=16\mu F$. The capacity of a set of capacitors connected in series satisfies

$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$.

By further solving,

$\frac{1}{C}=\frac{C_1{C}_2+C_2{C}_3+C_1{C}_3}{C_1{C}_2{C}_3}$'

or

$C=\frac{C_1{C}_2{C}_3}{C_1{C}_2+C_2{C}_3+C_1{C}_3}$

Substituting the given values we find the following

$C=3\mu F$.