(a) For two inductors in series as in Fig. 6.81(a), show that the current-division principle is
v_{1}=\frac{L_{1}}{L_{1}+L_{2}} v_{s}, \quad v_{2}=\frac{L_{2}}{L_{1}+L_{2}} v_{s}assuming that the initial conditions are zero.
(b) For two inductors in parallel as in Fig. 6.81(b), show that the current-division principle is
i_{1}=\frac{L_{2}}{L_{1}+L_{2}} i_{s}, \quad \mathrm{i}_{2}=\frac{L_{1}}{L_{1}+L_{2}} i_{s}assuming that the initial conditions are zero.