simulate this circuit – Schematic created using CircuitLab
When iI am using Thevenin's circuit and deriving inductor currents equations i am getting different Time constant \$ \tau\$ from what iI am getting when iI use Node Current analysis.
Here is my work for Thevenin's Circuit:-
\$from\ KVL :\$
\$V_{th} = i*R_{th} + L*\frac{di(t)}{dt}\$
\$\frac{V_{th}}{L}\ = i*\frac{R_{th}}{L}\ + \frac{di(t)}{dt}\$
Now after solving the homogeneous equation iI get
\$i(t)= A*e^{-\frac{t}{\tau}\ \hspace{35pt} Where\: A\: is\: Constant}\$
\$ \tau = \frac{L}{R_{Th}}\ = \frac{0.8}{8}\ = 0.1s \$
This is what iI am getting from Thevenin's equivalent circuit now Look at Original Circuit Equation
\$from\ KCL\: at\ node\: A :\$
\$ \frac{V_s-v}{R1}\ + \frac{0-v}{R2}\ - i = 0 \$
\$ \frac{V_s}{10}\ - v*(\ \frac{1}{10}\ +\frac{1}{40}\ ) - i =0 \$
\$ 8*v+i = \frac{V_s}{10}\ \$
\$ now\qquad v = L*\frac{di(t)}{dt}\ \$
\$ \frac{di(t)}{dt}\ + \frac{i}{8L}\ = \frac{V_s}{80L}\ \$
Now solving homogeneous equation
\$ \frac{di(t)}{dt}\ = - \frac{i}{8L}\ \$
\$i(t)= A*e^{-\frac{t}{\tau}\ \hspace{35pt} Where\: A\: is\: Constant}\$
\$ \tau = L*8 = 0.8*8 = 6.4s \$
Now here i am getting different \$ \tau \$ from what i get in thevenin'sThevenin's circuit...also source is just constant. pleasePlease tell me where i mI'm making mistake.
