Two capacitors, a 20 µF and a 30 µF, are connected in series. The total capacitance is:

• A. 0.083 µF
• B. 50 µF
• C. 12 µF
• D. 0.02 µF

Answer: (C)

When capacitors are connected in series, the total capacitance can be calculated using the formula:

[

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

]

where (C_1) and (C_2) are the capacitances of the individual capacitors. In this case, for a 20 µF capacitor and a 30 µF capacitor, the calculation would be as follows:

1. Convert the values into reciprocal form:

[

\frac{1}{C_{total}} = \frac{1}{20} + \frac{1}{30}

]

2. Find a common denominator, which is 60 in this case:

[

\frac{1}{C_{total}} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60}

]

3. Simplify the sum:

[

\frac{1}{C_{total}} = \frac{5}{60} = \frac{1}{12}

]

4. Taking the reciprocal gives the total capacitance:

\