Ham Radio General Class Practice Test

What is the capacitance of three 100 microfarad capacitors connected in series?

1. 0.30 microfarads

2. 0.33 microfarads

3. 33.3 microfarads

4. 300 microfarads

The correct answer is: 33.3 microfarads

When capacitors are connected in series, the total capacitance can be calculated using the formula: \[ \frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \] In this case, all three capacitors have the same capacitance of 100 microfarads. Plugging the values into the formula gives: \[ \frac{1}{C_{total}} = \frac{1}{100 \mu F} + \frac{1}{100 \mu F} + \frac{1}{100 \mu F} = \frac{1}{100} + \frac{1}{100} + \frac{1}{100} = \frac{3}{100} \] Therefore, to find the total capacitance, you take the reciprocal of \(\frac{3}{100}\): \[ C_{total} = \frac{100}{3} \mu F \approx 33.33 \mu F \] This calculation confirms that the capacitance of three 100 microfarad capacitors connected in series is approximately 33.3 microfarads,