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:
Start with i = C * dv/dt.Solve: C = i / (dv/dt).Plug i = 1 A, dv/dt = 1 V/s ⇒ C = 1 F.
Verification / Alternative check:
Energy in a capacitor: W = 0.5 * C * V^2; unit consistency corroborates the farad definition but is not the primary definition.
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:
changing the voltage on the plates at the rate of 1 V per second when 1 A of current is flowing
Discussion & Comments