Which of the following expressions is correct with respect to the voltage across capacitors in serie

Question

Which of the following expressions is correct with respect to the voltage across capacitors in series?

Examoogle · Accepted Answer

$\frac{V_1}{V_2} = \frac{C_2}{C_1}$

Explanation: In a series circuit, the charge stored on each capacitor is equal because the total charge supplied by the source must pass through each capacitor. Since $Q = CV$ and $Q$ is constant, the voltage across each capacitor is inversely proportional to its capacitance.

Working Principle: When capacitors are connected in series, the same charging current flows through each, resulting in identical displacement charge $Q$ on each capacitor plate. From the relationship $V = \frac{Q}{C}$, it follows that $V_1 = \frac{Q}{C_1}$ and $V_2 = \frac{Q}{C_2}$. Taking the ratio $\frac{V_1}{V_2} = \frac{Q/C_1}{Q/C_2}$, the charge $Q$ cancels out, yielding $\frac{V_1}{V_2} = \frac{C_2}{C_1}$.

Key Formulas: $V_i = V_{total} \cdot \frac{C_{eq}}{C_i}$ — Voltage division formula for capacitors; $\frac{V_1}{V_2} = \frac{C_2}{C_1}$ — Inverse proportionality relation

Key Points: Charge $Q$ is constant for all capacitors in a series circuit.; Voltage distribution across series capacitors is inversely proportional to their individual capacitance values.; The capacitor with the smallest capacitance experiences the largest voltage drop.

Advantages: Allows voltage sharing across components.; Useful for increasing the effective voltage rating of a capacitive bank.

Disadvantages: Reduces the total equivalent capacitance ($C_{eq}; Voltage distribution can be unequal if capacitances are not perfectly matched.

Applications: HVDC transmission systems for voltage grading.; Filtering circuits where specific voltage division is required.

Additional Info: This inverse relationship is analogous to the current division in parallel resistors.. Option B represents direct proportionality, which is incorrect.. Option D is an incorrect rearrangement of the equality; it should be $V_1 C_1 = V_2 C_2$ if $Q$ is constant.

Answer: A is correct — The ratio of voltages across capacitors in series is inversely proportional to their respective capacitance values.

Exam Tip: Always remember: Capacitors in series act like resistors in parallel (in terms of math/division), and capacitors in parallel act like resistors in series.

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