Key Idea Apply Kirchhoff' second law also called loop rule.
The algebraic sum of the changes in potential in complete transversal of a mesh (closed loop) is zero. $i e, \Sigma \mathrm{V}=0$
Here $\varepsilon_1-\left(i_1+i_2\right) R-i_1 r_1=0$
If there are $n$ meshes in a circuit, the number of independent equations in accordance with loop law will be $(n-1)$.