Capacitors in parallel – Compare equivalent to individual values Statement: “Total parallel capacitance is less than that of the smallest capacitor in parallel.” Determine correctness.

Introduction / Context:
Knowing how capacitors combine is essential for filter design, decoupling, and tuning networks. Parallel and series combinations behave oppositely, and mixing them up leads to large design errors.

Given Data / Assumptions:

• Ideal capacitors without significant parasitic inductance or resistance.
• Capacitors connected strictly in parallel across the same two nodes.
• Capacitance values are positive and finite.

Concept / Approach:

For capacitors in parallel, capacitances add: C_eq = C1 + C2 + ... + Cn. Therefore, the equivalent is greater than each individual capacitor and certainly greater than the smallest one. The given statement claims the opposite and is incorrect.

Step-by-Step Solution:

Verification / Alternative check:

Energy perspective: for a given voltage V, stored energy in the bank is (1/2) * C_eq * V^2, which increases as more capacitors are added in parallel, confirming the additive behavior.

Why Other Options Are Wrong:

Invoking dielectric type, frequency, or plate area does not reverse the ideal rule; parasitics may alter high-frequency impedance but not the DC/low-frequency capacitance sum in true parallel.

Common Pitfalls:

Confusing series and parallel rules: series reduces overall capacitance (below the smallest value), while parallel increases it (above the largest value).

Final Answer:

False.