Ham Radio General Class Practice Test

What is the capacitance of a 20 microfarad capacitor in series with a 50 microfarad capacitor?

1. 0.07 microfarads

2. 14.3 microfarads

3. 70 microfarads

4. 1000 microfarads

The correct answer is: 14.3 microfarads

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 scenario, we have a 20 microfarad capacitor and a 50 microfarad capacitor. Substituting the values into the formula: \[ \frac{1}{C_{total}} = \frac{1}{20 \, \mu F} + \frac{1}{50 \, \mu F} \] To solve this, first, convert each term to a common denominator: \[ \frac{1}{C_{total}} = \frac{5}{100} + \frac{2}{100} = \frac{7}{100} \] Now, inverse the sum to find the total capacitance: \[ C_{total} = \frac{100}{7} \] Calculating this gives approximately: \[ C_{total} \approx 14.2857 \, \mu F \] Rounding to one