When capacitors are connected in series, which of the following rules are applied?

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Examoogle · Accepted Answer

Voltage divider

Explanation: When capacitors are connected in series, the total voltage applied across the combination is distributed across individual capacitors based on their capacitive reactance. This phenomenon is known as the voltage divider rule for capacitors.

Working Principle: In a series circuit, the charge stored on each capacitor is identical, i.e., $Q = C_1V_1 = C_2V_2$. Since $V = Q/C$, the voltage across a specific capacitor $C_i$ in a series string of $n$ capacitors is $V_i = V_{total} 	imes \frac{C_{eq}}{C_i}$. Thus, the voltage divides inversely proportional to the capacitance values.

Key Formulas: $V_n = V_{total} 	imes \frac{C_{eq}}{C_n}$ — Voltage across nth capacitor in series; $\frac{1}{C_{eq}} = \sum \frac{1}{C_i}$ — Equivalent capacitance for series capacitors

Key Points: The charge on all series-connected capacitors remains the same ($Q_{total} = Q_1 = Q_2 = ... = Q_n$).; Smaller capacitance values will have a larger voltage drop across them in a series configuration.; Current divider rule applies to parallel-connected components, not series capacitors.

Advantages: Allows voltage rating of the circuit to exceed individual capacitor ratings.; Used in capacitive instrumentation and potential dividers.

Disadvantages: Equivalent capacitance is always smaller than the smallest individual capacitor.; Voltage distribution depends on precision of capacitance values.

Applications: High-voltage capacitor banks.; Coupling circuits where voltage sharing is necessary.

Additional Info: The voltage divider rule for capacitors is inverse to that of resistors because $C$ is in the denominator of the impedance formula $X_C = \frac{1}{j\omega C}$.. Option B is incorrect because current divider applies to parallel circuits where voltages are equal across branches.

Answer: A is correct — Capacitors in series act as a voltage divider because the applied voltage splits among them inversely proportional to their individual capacitance values.

Exam Tip: Always remember: Capacitors follow inverse rules compared to resistors (e.g., Series Capacitors = Parallel Resistors).

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