# Find resistance, inductance, and the time constant for an RL circuit.

1. The problem statement, all variables and given/known data

A 5.0V battery is attached to an RL circuit. The current is given by the formula: I = V0/R(1-e-t/τ), where I0 is the steady-state current, and τ is the time constant for the circuit.

Using the data table provided, determine τ, R, and L for this circuit.

Code:

``` I(mA) | t(μs) ---------------   0  |  0  3.94  |  1  6.32  |  2  7.77  |  3  8.65  |  4  9.18  |  5  9.50  |  6   ...  |  ...  10.0  |  ∞```

2. Relevant equations

I = V/R
τ = R/L
εL = -ε0e-Rt/L
I = ε0/R(1-e-Rt/L)

3. The attempt at a solution

So I started by concluding that ε0 = V0 = 5 V and I0 = 10 mA.

Using that I determined that R = V0/I0 = 5/0.01 = 500 Ω which gives me resistance.

I know that once I find τ or L I can easily find the other one, but I can’t figure out how to find either of them. At first I thought I could simply work I = V0/R(1-e-t/τ) algebraically to give me τ, but I end up getting undefined from using the natural log with a negative number.

I feel like I have to use the data to find one of them (probably τ?) by using the relationship between two of the data points but I’m sort of stuck at this point.

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