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Zorluk: OrtaFundamental and Derived Units

Which of the following combinations of fundamental SI base units is equivalent to the volt (V\text{V}), the SI unit of electric potential difference?

  1. kg⋅m2⋅s−3⋅A−1\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1}Cevap
  2. B
    kg⋅m2⋅s−2⋅A−1\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-1}
  3. C
    kg⋅m2⋅s−3⋅A\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}
  4. D
    kg⋅m⋅s−2⋅A−1\text{kg}\cdot\text{m}\cdot\text{s}^{-2}\cdot\text{A}^{-1}

Cevap

kg⋅m2⋅s−3⋅A−1\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1}
Electric potential difference (VV) is defined as work done (WW) per unit charge (QQ), giving V=WQV = \frac{W}{Q}. In fundamental SI units, work is kg⋅m2⋅s−2\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2} and electric charge is A⋅s\text{A}\cdot\text{s}. Dividing work by charge yields kg⋅m2⋅s−2A⋅s=kg⋅m2⋅s−3⋅A−1\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}.

Adım Adım Çözüm

1
State the defining physical equation for electric potential difference.
V=WQV = \frac{W}{Q}, where VV is electric potential, WW is work done in joules, and QQ is electric charge in coulombs.
Electric potential difference is defined as work done per unit electric charge.
2
Express work (WW) in terms of fundamental SI base units.
W=Force×distance=(kg⋅m⋅s−2)×m=kg⋅m2⋅s−2W = \text{Force} \times \text{distance} = (\text{kg}\cdot\text{m}\cdot\text{s}^{-2}) \times \text{m} = \text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}.
Work is the product of force and displacement, where force is mass times acceleration.
3
Express electric charge (QQ) in terms of fundamental SI base units.
Q=I×t=A⋅sQ = I \times t = \text{A}\cdot\text{s}.
Electric charge is defined as electric current multiplied by time.
4
Divide the base units of work by the base units of electric charge.
V=kg⋅m2⋅s−2A⋅s=kg⋅m2⋅s−3⋅A−1V = \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}.
Simplifying the exponents gives the equivalent combination of fundamental SI base units.

Anahtar Kavram

Expressing derived SI units in terms of fundamental (base) SI units.
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Konular

Fundamental and Derived Units

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