How do you calculate inductors in series and parallel

This post answers the question: “How do you calculate inductors in series and parallel?”.

Let’s consider series connection of two inductors depicted below.

Current through each conductor in the series connection $i\left(t\right)=\frac{{\lambda }_1\left(t\right)}{L_1}=\frac{{\lambda }_2\left(t\right)}{L_2}$, the total flux here $\lambda \left(t\right)={\lambda }_1\left(t\right)+{\lambda }_2\left(t\right)$. It means that effective inductance $L=\frac{\lambda \left(t\right)}{i\left(t\right)}=\frac{{\lambda }_1\left(t\right)+{\lambda }_2\left(t\right)}{{\displaystyle \frac{{\lambda }_1\left(t\right)}{L_1}}}=L_1+L_1\frac{{\lambda }_2\left(t\right)}{{\lambda }_1\left(t\right)}=L_1+L_2$.

Let’s now consider parallel combination of two inductors depicted below.

As soon as these inductors have equal voltage we can write that $\lambda \left(t\right)=L_1{i}_1\left(t\right)=L_2{i}_2\left(t\right)$. At the same time $i\left(t\right)=i_1\left(t\right)+i_1\left(t\right)$. From here we can obtain $\frac{1}{L}=\frac{i_1\left(t\right)+i_2\left(t\right)}{L_1{i}_1\left(t\right)}=\frac{1}{L_1}+\frac{1}{L_1}\frac{i_2\left(t\right)}{i_1\left(t\right)}=\frac{1}{L_1}+\frac{1}{L_2}=\frac{L_1{L}_2}{L_1+L_2}$.

More educational content can be found at Reddit community r/ElectronicsEasy.