Question

Which of the following is not a dimensionless quantity ?

• A. Quality factor
• B. Power factor
• C. Relative magnetic permeability (\(\mu_r\))
• D. Permeability of free space (\(\mu_0\))

Hint:

Remember that any quantity defined as a ratio of two other quantities with the same units (like relative density, relative permeability, strain, etc.) will be dimensionless. Also, arguments of trigonometric, logarithmic, and exponential functions must be dimensionless.

Answer 1

The Correct Option is D

To identify which of the given options is not a dimensionless quantity, it is important to understand what a dimensionless quantity means. A dimensionless quantity is one that does not have any physical dimension and is therefore expressed as a pure number.

1. Quality factor: The Quality factor (Q) is a dimensionless quantity that measures the sharpness of resonance of a system. It is calculated as the ratio of the resonant frequency to the bandwidth. Since it does not have any physical dimensions, this is a dimensionless quantity.
2. Power factor: The Power factor is also a dimensionless quantity. It is defined as the cosine of the phase angle between the voltage and current in an AC circuit. Being a ratio, it inherently does not have any units or dimensions.
3. Relative magnetic permeability (\(\mu_r\)): This is another dimensionless quantity. Relative permeability is the ratio of the permeability of a material to the permeability of free space (vacuum). As it is a ratio of two similar quantities, it is dimensionless.
4. Permeability of free space (\(\mu_0\)): The permeability of free space, often denoted by \(\mu_0\), is a physical constant that represents the absolute physical quantity of magnetic permeability in a classical vacuum. Its unit is Henry per meter (H/m), which means it has dimensions and is not dimensionless.

Based on the analysis, we can conclude that the correct answer is: Permeability of free space (\(\mu_0\)), which is not a dimensionless quantity, unlike the other options.