Capacitance definition: a farad is the capacitance that changes the plate voltage at 1 V per second when 1 A flows (i.e., C = I / (dV/dt)).

Introduction / Context:Capacitance measures a capacitor’s ability to store charge per unit voltage. In time-domain terms, current through a capacitor equals C times the rate of change of voltage. This definition leads directly to a practical unit statement for the farad (F).

Given Data / Assumptions:

• Ideal capacitor with capacitance C.
• Relation i(t) = C * dv(t)/dt.
• We interpret the SI unit definition in terms of current and voltage rate of change.

Concept / Approach:

• From i = C * dv/dt, rearrange to C = i / (dv/dt).
• Set i = 1 A and dv/dt = 1 V/s to obtain C = 1 F.
• This avoids misconceptions about energy or phase limits.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Dissipating 1 W: Ideal capacitors do not dissipate real power in steady sinusoidal excitation.
• Phase shift > 90°: For linear time-invariant networks, capacitors alone produce 90°, not > 90°.
• Storing 1 V for 1 s: Voltage is not 'stored' as a time product; that phrasing is incorrect.
• None of the above: Incorrect because option D states the standard definition.

Common Pitfalls:

• Confusing current-voltage rate relation with energy or power directly.
• Misinterpreting '1 farad' as a fixed energy quantity rather than a proportionality between charge and voltage.

Final Answer: