Question

10. An inductor with a$2.0\text{A}$ current stores energy. At what current will the stored energy be twice as large?

Short answer

The stored energy will be twice the initial store energy at 2.8 A current.

Step-by-step solution

Step 1. Given information

Initial current is$i_i=2\text{A}$

Step 2. Explanation

The initial energy stored in the inductor is

$U_i=\frac{1}{2}L{i}_i^2$

And the final energy stored in the inductor is

$U_f=\frac{1}{2}L{i}_f^2$

The final energy is twice the initial energy, hence,

$\begin{array}{l}{U}_f=2U_i\\ \Rightarrow \frac{U_f}{U_i}=2\\ \frac{\frac{1}{2}L{i}_f^2}{\frac{1}{2}{L}_i^2}=2\\ \Rightarrow i_f^2=2i_i^2\\ \Rightarrow i_f=\sqrt{2}{i}_i\\ i_f=\sqrt{2}(2.0\text{A})=2.8\text{A}\end{array}$

The stored energy will be twice the initial store energy at 2.8 A current.