What is the total capacitance of two capacitors of 4 microfarads and 6 microfara

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Question: What is the total capacitance of two capacitors of 4 microfarads and 6 microfarads connected in series? (2019)

Options:

Correct Answer: 2.4 microfarads

Exam Year: 2019

Solution:

For capacitors in series, 1/C_eq = 1/C1 + 1/C2. Thus, 1/C_eq = 1/4 + 1/6 = 5/12. Therefore, C_eq = 2.4 microfarads.

What is the total capacitance of two capacitors of 4 microfarads and 6 microfarads connected in series? (2019)

What is the total capacitance of two capacitors of 4 microfarads and 6 microfarads connected in series? (2019)

Step 1: Identify the values of the capacitors. We have C1 = 4 microfarads and C2 = 6 microfarads.
Step 2: Use the formula for capacitors in series: 1/C_eq = 1/C1 + 1/C2.
Step 3: Substitute the values into the formula: 1/C_eq = 1/4 + 1/6.
Step 4: Find a common denominator for the fractions. The common denominator for 4 and 6 is 12.
Step 5: Rewrite the fractions with the common denominator: 1/4 = 3/12 and 1/6 = 2/12.
Step 6: Add the fractions: 1/C_eq = 3/12 + 2/12 = 5/12.
Step 7: To find C_eq, take the reciprocal of 5/12: C_eq = 12/5.
Step 8: Calculate 12/5, which equals 2.4 microfarads.

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