Question
What is the capacitance of a 20-microfarad capacitor connected in series with a 50-microfarad capacitor?
Answer Options
- A) 0.07 microfarads
- B) 14.3 microfarads
- C) 70 microfarads
- D) 1,000 microfarads
Correct Answer: B
Explanation
For capacitors connected in series, the total capacitance (C_T) is calculated using the product-over-sum formula, similar to two resistors in parallel: C_T = (C_1 \times C_2) / (C_1 + C_2).
Using the given values, C_1 = 20 \text{ }\mu\text{F} and C_2 = 50 \text{ }\mu\text{F}: C_T = \frac{20 \text{ }\mu\text{F} \times 50 \text{ }\mu\text{F}}{20 \text{ }\mu\text{F} + 50 \text{ }\mu\text{F}} = \frac{1000}{70} \approx 14.28 \text{ }\mu\text{F.} The total capacitance of the series circuit is 14.3 \text{ microfarads}.
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