What is the equivalent capacitance of two capacitors, 4 µF and 6 µF, in series?

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Question: What is the equivalent capacitance of two capacitors, 4 µF and 6 µF, in series?

Options:

Correct Answer: 2.4 µF

Solution:

1/C_total = 1/C1 + 1/C2 = 1/4 + 1/6 = 5/12, thus C_total = 12/5 = 2.4 µF.

What is the equivalent capacitance of two capacitors, 4 µF and 6 µF, in series?

What is the equivalent capacitance of two capacitors, 4 µF and 6 µF, in series?

Step 1: Identify the values of the capacitors. We have C1 = 4 µF and C2 = 6 µF.
Step 2: Use the formula for capacitors in series: 1/C_total = 1/C1 + 1/C2.
Step 3: Substitute the values into the formula: 1/C_total = 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_total = 3/12 + 2/12 = 5/12.
Step 7: To find C_total, take the reciprocal of 5/12: C_total = 12/5.
Step 8: Calculate 12/5 to get C_total = 2.4 µF.

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