If a capacitor of 10 µF is connected in series with a 20 µF capacitor, what is t

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Question: If a capacitor of 10 µF is connected in series with a 20 µF capacitor, what is the total capacitance?

Options:

Correct Answer: 6.67 µF

Solution:

1/C_total = 1/C1 + 1/C2 = 1/10 + 1/20 = 3/20, thus C_total = 20/3 µF = 6.67 µF.

If a capacitor of 10 µF is connected in series with a 20 µF capacitor, what is the total capacitance?

If a capacitor of 10 µF is connected in series with a 20 µF capacitor, what is the total capacitance?

Step 1: Identify the values of the capacitors. We have C1 = 10 µF and C2 = 20 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 = 1/10 + 1/20.
Step 4: Find a common denominator to add the fractions. The common denominator for 10 and 20 is 20.
Step 5: Rewrite the fractions: 1/10 = 2/20 and 1/20 = 1/20.
Step 6: Add the fractions: 1/C_total = 2/20 + 1/20 = 3/20.
Step 7: To find C_total, take the reciprocal of 3/20: C_total = 20/3 µF.
Step 8: Calculate 20/3 to get the final answer: C_total = 6.67 µF.

Capacitance in Series – When capacitors are connected in series, the total capacitance is found using the formula 1/C_total = 1/C1 + 1/C2.