1. Concept: Derived SI units can be unspooled into their fundamental base components using standard physics formulas.
2. Formula: $$ C = \frac{Q}{V} \quad \text{where} \quad Q = I t \quad \text{and} \quad V = \frac{W}{Q} $$
3. Solution: - Start with Farad: \( \text{F} = \frac{\text{Coulombs (C)}}{\text{Volts (V)}} \).
- Expand Volt (V = Joules/Coulomb): \( \text{F} = \frac{\text{C}}{\text{J/C}} = \frac{\text{C}^2}{\text{J}} \).
- Expand Joule (J = Newton \( \times \) meter): \( \text{F} = \frac{\text{C}^2}{\text{N m}} \).
- Expand Coulomb (C = Ampere \( \times \) second): \( \text{F} = \frac{(\text{A s})^2}{\text{N m}} = \frac{\text{A}^2 \text{s}^2}{\text{N m}} \).
4. Why other options are incorrect: Options B, C, and D contain incorrect powers for the Ampere (A) or seconds (s) terms, failing the dimensional analysis derivation.
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