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Difficulty: MediumFundamental and Derived Quantities

Match each physical quantity listed on the left with its corresponding SI classification and base unit representation on the right.

  • Electric currentFundamental quantity measured in amperes (A\text{A})
  • Thermodynamic temperatureFundamental quantity measured in kelvins (K\text{K})
  • Electric potential differenceDerived quantity expressed in SI base units as kg⋅m2⋅s−3⋅A−1\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1}
  • Specific heat capacityDerived quantity expressed in SI base units as m2⋅s−2⋅K−1\text{m}^2\cdot\text{s}^{-2}\cdot\text{K}^{-1}

Answer

Electric current matches Fundamental quantity measured in amperes; Thermodynamic temperature matches Fundamental quantity measured in kelvins; Electric potential difference matches Derived quantity expressed as kg·m²·s⁻³·A⁻¹; Specific heat capacity matches Derived quantity expressed as m²·s⁻²·K⁻¹.
Electric current and thermodynamic temperature are basic SI fundamental quantities. Electric potential difference and specific heat capacity are derived quantities whose fundamental unit decompositions follow directly from their governing formulas.

Step-by-Step Solution

1
Identify fundamental physical quantities and their base units
Electric current and thermodynamic temperature are fundamental SI quantities with base units ampere (A\text{A}) and kelvin (K\text{K}) respectively.
Fundamental physical quantities are defined independently and serve as the foundation for the SI system.
2
Decompose electric potential difference into SI base units
Electric potential difference V=WorkCharge=kg⋅m2⋅s−2A⋅s=kg⋅m2⋅s−3⋅A−1V = \frac{\text{Work}}{\text{Charge}} = \frac{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}}{\text{A}\cdot\text{s}} = \text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1}.
Because it is expressed by combining fundamental quantities, it is a derived quantity.
3
Decompose specific heat capacity into SI base units
Specific heat capacity c=EnergyMass×Temperature change=kg⋅m2⋅s−2kg⋅K=m2⋅s−2⋅K−1c = \frac{\text{Energy}}{\text{Mass} \times \text{Temperature change}} = \frac{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}}{\text{kg}\cdot\text{K}} = \text{m}^2\cdot\text{s}^{-2}\cdot\text{K}^{-1}.
It is calculated from energy, mass, and temperature, making it a derived quantity.

Key Concept

Fundamental quantities are independent basic quantities, whereas derived quantities are formed through algebraic combination of fundamental quantities.
Estimated Time:1m 30s
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Topics

Fundamental and Derived Quantities

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