Inductance Formula of busbars

The inductance of a busbar can be calculated using various methods depending on the geometry and configuration of the busbar. For simple shapes like rectangular or cylindrical conductors, you can use formulas derived from electromagnetic theory.

For a rectangular busbar with width $𝑤$, thickness $𝑡$, and length $𝐿$, the inductance per unit length ${𝐿}^{\mathrm{\prime }}$ can be approximated using the formula:

${𝐿}^{\mathrm{\prime }}=\frac{𝜇\cdot 𝑤\cdot (\ln \left(\frac{2𝐿}{𝑤}\right)-0.75)}{𝜋}$

Where:

• $𝜇$ is the permeability of the material (typically air or the material surrounding the busbar),
• $𝑤$ is the width of the busbar,
• $𝑡$ is the thickness of the busbar, and
• $𝐿$ is the length of the busbar.

For a cylindrical busbar with radius $𝑟$ and length $𝐿$, the inductance per unit length ${𝐿}^{\mathrm{\prime }}$ can be approximated as:

${𝐿}^{\mathrm{\prime }}=\frac{𝜇\cdot 𝐿}{2𝜋}(\ln \left(\frac{2𝐿}{𝑟}\right)-1)$

These formulas are approximate and may vary depending on factors such as the proximity of other conductors, the presence of magnetic materials nearby, and the frequency of the current flowing through the busbar. For more accurate results, finite element analysis (FEA) or electromagnetic simulation software may be employed.