Answer to Question #308738 in Electric Circuits for stuti

Question

Find out the inductor current equation for an RL circuit with step response, assume the initial current through the inductor is 𝐼0.

Answer 1

Circuit equation

$$0=iR+L\frac{di}{dt}$$

Solution to this equation

$$i=Ae^{-t/\tau}$$

Where $A - constant, \tau = L/R$

Initial conditions t=0; i=I0

Then $A=I_0$

Answer

$$i=I_0e^{-\frac{t}{\tau}}$$