Which among the following expressions relate charge, voltage and capacitance of a capacitor?

Question

Examoogle · Accepted Answer

$Q = CV$

Explanation: The relationship between electric charge, voltage, and capacitance is governed by the definition of capacitance as the ability of a body to store an electrical charge. Mathematically, it states that the charge $Q$ stored in a capacitor is directly proportional to the potential difference $V$ across its plates, where the proportionality constant is the capacitance $C$.

Working Principle: When a voltage source is connected across a capacitor, the potential difference creates an electric field that causes charge carriers to accumulate on the plates. The ratio of the magnitude of charge on either plate to the potential difference between them remains constant for a specific capacitor geometry and dielectric medium. Thus, $C = \frac{Q}{V}$, which rearranges to $Q = CV$.

Key Formulas: $Q = CV$ — Charge storage relationship; $C = \frac{\epsilon A}{d}$ — Capacitance based on physical dimensions

Key Points: Capacitance ($C$) is measured in Farads ($F$).; Charge ($Q$) is measured in Coulombs ($C$).; Voltage ($V$) is measured in Volts ($V$).; The relationship is linear; doubling the voltage doubles the stored charge for a fixed capacitor.

Advantages: Fundamental for designing energy storage circuits.; Essential for understanding filtering and timing circuits.

Disadvantages: Does not account for non-ideal leakage currents in real-world capacitors.

Applications: Power supply smoothing capacitors; Coupling and decoupling in signal processing

Additional Info: The unit of capacitance, the Farad, is defined as $1 F = 1 C/V$.. Options A and B represent incorrect algebraic manipulations of the fundamental formula $Q = CV$.

Answer: C is correct — The charge stored in a capacitor is the product of its capacitance and the voltage applied across it, expressed as $Q = CV$.

Exam Tip: Always remember the mnemonic 'Q is CV' (pronounced like 'Q is See-Vee') to quickly recall this fundamental identity in DC circuit analysis.

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