*Question G5C12:
What is the capacitance of a 20-microfarad capacitor connected in series with a 50-microfarad capacitor?*  

*Correct Answer is  B: 14.3 microfarads*  

### AI Response: (may contain errors)  

To find the total capacitance of capacitors connected in series, we use the formula:

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

where:
- $C_{total}$ is the total capacitance,
- $C_1$ is the capacitance of the first capacitor,
- $C_2$ is the capacitance of the second capacitor.

In this case:
- $C_1 = 20 \, \mu F$ (microfarads)
- $C_2 = 50 \, \mu F$

Substituting the values into the formula:

$$
\frac{1}{C_{total}} = \frac{1}{20} + \frac{1}{50}
$$

To add these fractions, we need a common denominator. The least common multiple of 20 and 50 is 100. Thus, we convert the fractions:

$$
\frac{1}{20} = \frac{5}{100} \quad \text{and} \quad \frac{1}{50} = \frac{2}{100}
$$

Now we can add them:

$$
\frac{1}{C_{total}} = \frac{5}{100} + \frac{2}{100} = \frac{7}{100}
$$

Taking the reciprocal gives us the total capacitance:

$$
C_{total} = \frac{100}{7} \approx 14.3 \, \mu F
$$

### Explanation of the Correct Answer:
- The correct answer is **14.3 microfarads** because we correctly applied the series capacitance formula and calculated the total capacitance.

### Why the Other Choices are Incorrect:
- **A: 0.07 microfarads**: This value is too low and does not reflect the correct calculation.
- **C: 70 microfarads**: This value is incorrect because it suggests a parallel connection, which is not the case here.
- **D: 1,000 microfarads**: This value is far too high and does not correspond to any reasonable calculation for capacitors in series.

### Summary:
- For capacitors in series, always use the reciprocal formula.
- The total capacitance will always be less than the smallest capacitor in the series.