$4.$ A coupled inductor circuit is shown below.

I guie IJ$\mathrm{.}0$L For rrod. $19\mathrm{.}12.$

a$.$ If a $10$ ohm resistor is placed between nodes $"\backslash ($ a $\backslash )"$ and $"$b$"$ as shown in the figure, write the mesh equations needed to solve for the voltage across the $10$ ohm resistor. No need to solve, just write the equations. Let $\backslash ($ I$\_\{1\}\backslash )$ be the current in the mesh that contains the voltage source and let $\backslash ($ I$\_\{2\}\backslash )$ be the current in the mesh that contains the a$-$b terminal pair and the $10$ ohm resistor. Currents should be in the clockwise direction

b$.$ What is the coupling coefficient $"\backslash ($ k $\backslash )"$ for the two inductors.