What is the total capacitance of capacitors rated at 10 microfarads, 25 microfarads, and 40 microfarads connected in series?

To determine the total capacitance of capacitors connected in series, the formula to use is:

[

\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}

]

where ( C_1 ), ( C_2 ), and ( C_3 ) are the capacitances of the individual capacitors. In this case, we have capacitors rated at 10 microfarads, 25 microfarads, and 40 microfarads.

Substituting the values into the formula gives:

[

\frac{1}{C_{total}} = \frac{1}{10} + \frac{1}{25} + \frac{1}{40}

]

To add these fractions, a common denominator is needed. The least common multiple of 10, 25, and 40 is 200. Thus, we can rewrite the fractions:

[

\frac{1}{10} = \frac{20}{200}, \quad \frac{1}{25} = \frac{8}{200}, \quad \frac{1}{40} = \