When capacitors are connected in parallel, the total capacitance is always __________ the individual

Question

When capacitors are connected in parallel, the total capacitance is always __________ the individual capacitance values.

Examoogle · Accepted Answer

Greater than

Explanation: When capacitors are connected in parallel, the total equivalent capacitance is the arithmetic sum of the individual capacitances. Consequently, the equivalent capacitance is always greater than any single capacitor used in the parallel network.

Working Principle: In a parallel connection, every capacitor is connected to the same potential difference (voltage). Since $Q = CV$, the total charge stored is the sum of charges on each capacitor ($Q_{total} = Q_1 + Q_2 + ... + Q_n$). Substituting $Q = CV$ yields $C_{eq}V = C_1V + C_2V + ... + C_nV$, which simplifies to $C_{eq} = C_1 + C_2 + ... + C_n$.

Key Formulas: $C_{eq} = \sum_{i=1}^{n} C_i$ — Summation formula for parallel capacitors; $Q_{total} = C_{eq}V$ — Total charge relation in parallel circuits

Key Points: Voltage remains constant across all parallel branches.; The total plate area effectively increases in a parallel connection.; The equivalent capacitance is always greater than the largest individual capacitor in the group.; Parallel connection is used to increase the total energy storage capacity of the circuit.

Advantages: Increases total capacitance of the system.; Reduces the equivalent series resistance (ESR) of the capacitor bank.

Disadvantages: Requires more physical space for multiple components.; Risk of voltage imbalance if capacitor ratings are mismatched.

Applications: Power supply filtering to reduce ripple voltage.; Energy storage banks in pulsed power systems.; Bypass and decoupling applications in high-frequency circuits.

Additional Info: In contrast, capacitors in series lead to a reduction in total capacitance: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ... + \frac{1}{C_n}$.. Option B (Less than) describes capacitors in series, not parallel.

Answer: A is correct — The equivalent capacitance in a parallel circuit is the algebraic sum of individual values, which results in a value larger than any individual capacitor.

Exam Tip: Always remember: Capacitors in parallel behave like Resistors in series, while Capacitors in series behave like Resistors in parallel.

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