Is ohm a derived unit?
2 Answers
Yes, **ohm (Ω)** is a derived unit in the International System of Units (SI). It measures **electrical resistance** and is derived from the base units of **length (meter, m)**, **mass (kilogram, kg)**, **time (second, s)**, and **electric current (ampere, A)**.
The ohm is defined based on **Ohm's Law**, which states that:
\[
R = \frac{V}{I}
\]
Where:
- \( R \) is the resistance in ohms,
- \( V \) is the potential difference (voltage) in volts,
- \( I \) is the current in amperes.
From the relationship between these quantities, the unit of ohms can be expressed as:
\[
1 \, \Omega = \frac{1 \, \text{volt}}{1 \, \text{ampere}} = \frac{\text{m}^2 \cdot \text{kg}}{\text{s}^3 \cdot \text{A}^2}
\]
Thus, the ohm is derived from the fundamental SI units of measurement.
The ohm is defined based on **Ohm's Law**, which states that:
\[
R = \frac{V}{I}
\]
Where:
- \( R \) is the resistance in ohms,
- \( V \) is the potential difference (voltage) in volts,
- \( I \) is the current in amperes.
From the relationship between these quantities, the unit of ohms can be expressed as:
\[
1 \, \Omega = \frac{1 \, \text{volt}}{1 \, \text{ampere}} = \frac{\text{m}^2 \cdot \text{kg}}{\text{s}^3 \cdot \text{A}^2}
\]
Thus, the ohm is derived from the fundamental SI units of measurement.
Yes, the ohm is a derived unit of electrical resistance in the International System of Units (SI). It is named after the German physicist Georg Simon Ohm.
To understand why it's a derived unit, let's break it down:
1. **Definition**: The ohm (symbol: Ω) measures electrical resistance. It is defined as the resistance between two points of a conductor when a constant potential difference of one volt (V) applied across the conductor produces a current of one ampere (A).
2. **Formula**: Resistance (R) can be calculated using Ohm's Law:
\[ R = \frac{V}{I} \]
where \( V \) is the voltage in volts and \( I \) is the current in amperes.
3. **Base Units**: In terms of SI base units, the ohm can be expressed as:
\[ \text{Ohm} = \frac{\text{Volt}}{\text{Ampere}} \]
Since the volt is derived from the base units of the SI system as \( \text{Volt} = \text{Joule per Coulomb} = \text{(Kilogram} \cdot \text{meter}^2 \text{per second}^3) / \text{Coulomb} \), and the ampere is a base unit itself, the ohm is a derived unit based on these other units.
So, the ohm is derived from the base SI units of length (meter), mass (kilogram), time (second), and electric current (ampere).
To understand why it's a derived unit, let's break it down:
1. **Definition**: The ohm (symbol: Ω) measures electrical resistance. It is defined as the resistance between two points of a conductor when a constant potential difference of one volt (V) applied across the conductor produces a current of one ampere (A).
2. **Formula**: Resistance (R) can be calculated using Ohm's Law:
\[ R = \frac{V}{I} \]
where \( V \) is the voltage in volts and \( I \) is the current in amperes.
3. **Base Units**: In terms of SI base units, the ohm can be expressed as:
\[ \text{Ohm} = \frac{\text{Volt}}{\text{Ampere}} \]
Since the volt is derived from the base units of the SI system as \( \text{Volt} = \text{Joule per Coulomb} = \text{(Kilogram} \cdot \text{meter}^2 \text{per second}^3) / \text{Coulomb} \), and the ampere is a base unit itself, the ohm is a derived unit based on these other units.
So, the ohm is derived from the base SI units of length (meter), mass (kilogram), time (second), and electric current (ampere).