When capacitors are connected in series, the equivalent capacitance is ___________ each individual c

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When capacitors are connected in series, the equivalent capacitance is ___________ each individual capacitance.

Examoogle · Accepted Answer

Less then Explanation: When capacitors are connected in series, the equivalent capacitance is always less than the smallest individual capacitance in the network. This occurs because series connections effectively increase the total plate separation distance between the two ends of the capacitor chain. Working Principle: In a series circuit, the total charge $Q$ on each capacitor is identical, but the total applied voltage $V$ is the sum of the individual voltage drops across each capacitor. Given $V = \frac{Q}{C_{eq}} = V_1 + V_2 + ... + V_n$, substituting $V_i = \frac{Q}{C_i}$ results in the reciprocal addition formula $\frac{1}{C_{eq}} = \sum \frac{1}{C_i}$. Mathematically, this reciprocal sum forces the total equivalent capacitance to be smaller than any single value in the series. Key Formulas: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ... + \frac{1}{C_n}$ — Total equivalent capacitance for series; $V_{total} = V_1 + V_2 + ... + V_n$ — Kirchhoff's Voltage Law in series Key Points: The total capacitance in series is always less than the smallest individual capacitor.; Charge $Q$ remains constant across all capacitors in a series string.; The inverse of the equivalent capacitance is the algebraic sum of the inverses of individual capacitances.; Connecting capacitors in series is often used to increase the voltage rating of the combined capacitor bank. Advantages: Increased effective voltage rating of the bank; Useful for voltage division applications Disadvantages: Reduces the overall equivalent capacitance; Requires balancing resistors to ensure equal voltage distribution if leakage currents vary Applications: High-voltage capacitor banks; Coupling capacitors in RF circuits; Capacitive voltage dividers Additional Info: The option 'Less then' is a grammatical error in the source, but it remains the correct choice as it represents the physical phenomenon.. If all capacitors are equal ($C_1 = C_2 = ... = C_n = C$), then $C_{eq} = \frac{C}{n}$. Answer: B is correct — The equivalent capacitance in series is always lower than the smallest individual capacitor because the reciprocal addition decreases the overall effective capacitance. Exam Tip: Always remember that series capacitors act like parallel resistors, and parallel capacitors act like series resistors.

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