In the shown circuit, i₁=10 e − 2 t e^{-2t} e − 2 t A, i₂=4 A and V꜀=3 e − 2 t e^{-2t} e − 2 t V. If Vₗ=a e − b t e^{-bt} e − b t find a/b.
Physics · AC Circuits
JEE Advanced

Question

In the shown circuit, i₁=10 e − 2 t e^{-2t} e − 2 t A, i₂=4 A and V꜀=3 e − 2 t e^{-2t} e − 2 t V. If Vₗ=a e − b t e^{-bt} e − b t find a/b.

G1 Physics · Accepted Answer

Use KCL to obtain the inductor current from the given branch currents, then use Vₗ=L(diₗ/dt) with L=4 H. Writing the result as Vₗ=a e ( − b t ) e^(-bt) e ( − b t ) gives a/b=8.