# DC Transient RL Circuit - Current Decay

If I have a circuit with

R = 1Ω
L = 300μH
V = 20V
i0 = 5A

I know that I can use the equation at the bottom of page 13 to calculate the current rise given any starting current and input voltage:

i(t) = (V/R)[1-e-t/τ] + i0e-t/τ

This is fine, and stops increasing at 20A as expected, but then how would I (if I need to) arrange the equation so that it works in a similar way for decay? Say I was starting at a current of 15A, with a driving voltage of 10V?

I know that if I use:

i(t) = (V/R)[e-t/τ]

I will start decaying at 10A down to 0A, but I'm interested in being able to specify a negative voltage to drive the decay faster, with a variable starting current.

*edit*
Also, how would I work out when it is best to switch between building and decaying current? Would it just be when |V/R| > |i(t)| is less than 0, I build, and when |V/R| < |i(t)| I decay?

Thanks again

Last edited:

## Answers and Replies

axemaster
I don't understand the problem. That equation appears to work regardless of "rise" or "decay", and regardless of what types of inputs you use (provided they are not dynamic).