What is the base SI unit of voltage

Question

ScanSolve AI Tutor · Accepted Answer

The base SI unit of voltage is the Volt (V). We can express it in terms of base SI units using the definition of voltage as energy per unit charge.

Recall the definition of voltage ( $V$ ).
Voltage is the amount of energy ( $W$ ) per unit electric charge ( $Q$ ).
$V = \frac{W}{Q}$
Substitute the SI units for energy and charge.
- Energy ( $W$ ) is measured in Joules (J).
- Charge ( $Q$ ) is measured in Coulombs (C). So, $1 \, \text{V} = 1 \, \frac{\text{J}}{\text{C}}$ .
Express Joules (J) in terms of base SI units.
Energy is force times distance ( $W = F \cdot d$ ). Force ( $F$ ) is mass times acceleration ( $F = m \cdot a$ ).
$1 \, \text{J} = 1 \, \text{N} \cdot \text{m}$
And $1 \, \text{N} = 1 \, \text{kg} \cdot \text{m} \cdot \text{s}^{-2}$ .
Therefore,
$1 \, \text{J} = (1 \, \text{kg} \cdot \text{m} \cdot \text{s}^{-2}) \cdot \text{m} = 1 \, \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}$
Express Coulombs (C) in terms of base SI units.
From a previous problem, we know that charge is current times time ( $Q = I \cdot t$ ).
$1 \, \text{C} = 1 \, \text{A} \cdot \text{s}$
Substitute the base SI unit expressions for Joules and Coulombs back into the equation for Volts
$1 \, \text{V} = \frac{1 \, \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}}{1 \, \text{A} \cdot \text{s}}$
Simplify the expression
$1 \, \text{V} = 1 \, \text{kg} \cdot \text{m}^2 \cdot \text{A}^{-1} \cdot \text{s}^{-3}$
Therefore, the base SI unit of voltage (Volt) expressed in terms of base physical quantities is:
$\boxed{\text{1 V} = \text{1 kg} \cdot \text{m}^2 \cdot \text{A}^{-1} \cdot \text{s}^{-3}}$

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