Finding Time Constant T Without L for an LR Circuit

[boysenbeary]

Homework Statement

Obtain the time constant of the circuit.

- Fill-in the third column of the table with appropriate calculated values which result in a graph vs.
time that we expect to be a straight line.

- Make a plot of your computed third column numbers vs. time, and insert a best-fit line.

- Use the best-fit line to extract the time constant of the circuit.

Relevant Equations

$$I = {I_0} {e^{\frac{-t}{T}}}$$

$$T = \frac {L}{R}$$

$$V = R*I$$

$$R = 295.3 \Omega$$

$$I_0 = 0.01765 A$$

Edit: Picture of the Circuit (Simple RL circuit)

The value of L is not given.

Attempt to Solve for T by Rearranging Equation 1:

I rearranged the equation to solve for T, using Ohm's Law so solve for I = V/R at each time.

https://www.desmos.com/calculator/qlb2n6w4bg

This graph is non-linear, but the problem says to expect a linear graph?

Attempt to Use A Generic Ln(V) Graph:

https://www.desmos.com/calculator/ojvfgihyeq

This graph is linear but how do I know this is the right equation?

The point of this problem is to find the time constant T, then use that to solve for L

Would appreciate any guidance, thank you.

 

[boysenbeary]

I've complied 4 potential graphs that might lead to T, but I'm not sure if they are correct

https://www.desmos.com/calculator/lc51efsd3h (Linear)

https://www.desmos.com/calculator/nvtkccwj5k (Linear)

https://www.desmos.com/calculator/wu5sdvjatn (Linear)

https://www.desmos.com/calculator/gq1rrbryky (Non-Linear)

Any insights?

 

[Babadag]

I=V/R ;I=Io*e^(-t/T); ln(I)=ln(Io)-t/T
-t/T=ln(I)-ln(Io)
T=t/((ln(Io)-ln(I))
However, the "constant" T is not so constant. See the attached no.1
That means something is wrong.
If we shall change the time t [let's to add a 0.2 msec in all position] then the error will be 1% from average. See attached no.2