What is the total capacitance of two capacitors of 2 µF and 3 µF connected in se

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Question: What is the total capacitance of two capacitors of 2 µF and 3 µF connected in series? (2023)

Options:

Correct Answer: 1.2 µF

Exam Year: 2023

Solution:

For capacitors in series, 1/C_total = 1/C1 + 1/C2. Thus, 1/C_total = 1/2 + 1/3 = 5/6, so C_total = 1.2 µF.

What is the total capacitance of two capacitors of 2 µF and 3 µF connected in series? (2023)

What is the total capacitance of two capacitors of 2 µF and 3 µF connected in series? (2023)

Step 1: Identify the values of the capacitors. We have C1 = 2 µF and C2 = 3 µF.
Step 2: Use the formula for total capacitance in series: 1/C_total = 1/C1 + 1/C2.
Step 3: Substitute the values into the formula: 1/C_total = 1/2 + 1/3.
Step 4: Find a common denominator for the fractions. The common denominator for 2 and 3 is 6.
Step 5: Rewrite the fractions with the common denominator: 1/2 = 3/6 and 1/3 = 2/6.
Step 6: Add the fractions: 1/C_total = 3/6 + 2/6 = 5/6.
Step 7: To find C_total, take the reciprocal of 5/6: C_total = 6/5.
Step 8: Calculate 6/5, which equals 1.2 µF.

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