When different rated capacitors are connected in series in a circuit, the total capacitance is ________.

When different rated capacitors are connected in series in a circuit, the total capacitance is ________.

• A. Less than the capacitance of the lowest rated capacitor
• B. Greater than the largest capacitor
• C. Always the harmonic mean
• D. Equal to the average

Answer: (A)

In series, the same amount of charge must flow through every capacitor, and the voltages across each add up to the total voltage. The way to combine capacitors in series is C_eq = 1 / (1/C1 + 1/C2 + ...). Because each term 1/Ci is positive, the sum is larger than any individual 1/Ci, which makes C_eq smaller than any individual capacitance. So the overall capacitance is always less than the smallest capacitor in the chain (and only if all capacitors were identical would it equal that value). The harmonic mean is not how series capacitance combines, and the total cannot be greater than the largest capacitor—in fact it ends up smaller than the smallest.

In series, the same amount of charge must flow through every capacitor, and the voltages across each add up to the total voltage. The way to combine capacitors in series is C_eq = 1 / (1/C1 + 1/C2 + ...). Because each term 1/Ci is positive, the sum is larger than any individual 1/Ci, which makes C_eq smaller than any individual capacitance. So the overall capacitance is always less than the smallest capacitor in the chain (and only if all capacitors were identical would it equal that value). The harmonic mean is not how series capacitance combines, and the total cannot be greater than the largest capacitor—in fact it ends up smaller than the smallest.