How do you calculate total capacitance in a series circuit?

How do you calculate total capacitance in a series circuit?

• A. C_total = C1 + C2 + ...
• B. 1/C_total = 1/C1 + 1/C2 + ...
• C. C_total = C1 * C2
• D. C_total = (C1 * C2) / (C1 + C2)

Answer: (B)

In a series circuit, the total capacitance is calculated using the formula \( 1/C_{\text{total}} = 1/C1 + 1/C2 + ... \). This relationship arises because, in a series configuration, the charge stored on each capacitor is the same, while the total voltage across the combination is the sum of the individual voltages across each capacitor. This means that while each capacitor stores a certain amount of charge (dictated by its capacitance), the effective total "storage ability" of the combination decreases. Consequently, the reciprocal of the total capacitance is the sum of the reciprocals of each individual capacitance. This formula accurately reflects how capacitors interact in series and is fundamental to understanding how capacitance behaves in such arrangements.

In a series circuit, the total capacitance is calculated using the formula ( 1/C_{\text{total}} = 1/C1 + 1/C2 + ... ). This relationship arises because, in a series configuration, the charge stored on each capacitor is the same, while the total voltage across the combination is the sum of the individual voltages across each capacitor.

This means that while each capacitor stores a certain amount of charge (dictated by its capacitance), the effective total "storage ability" of the combination decreases. Consequently, the reciprocal of the total capacitance is the sum of the reciprocals of each individual capacitance. This formula accurately reflects how capacitors interact in series and is fundamental to understanding how capacitance behaves in such arrangements.