MHB Is this the correct approach for using Taylor series in this problem?

[Ironhorse1]

Hi there! I need a bit of help on a homework problem. The problem is about a voltage (V) across a circuit with a resistor (R) and and inductor (L). The current at time "t" is:

I= (V/R)^{(1/e^(-RT/L)}

And the problem asks me to use Taylor series to deduce that I is approximately equal to (Vt/L) if R is small.

I have started by trying to use the known Taylor Series expansion for the geometric series, (1/1-x) = 1+x+x^2+x^3+... replacing x with (V/R). I'm not sure what to do next, or if this was the right first step to take.

What do you think? I so very much appreciate any help!

 

[I like Serena]

Hi there! I need a bit of help on a homework problem. The problem is about a voltage (V) across a circuit with a resistor (R) and and inductor (L). The current at time "t" is:

I= (V/R)^{(1/e^(-RT/L)}

And the problem asks me to use Taylor series to deduce that I is approximately equal to (Vt/L) if R is small.

I have started by trying to use the known Taylor Series expansion for the geometric series, (1/1-x) = 1+x+x^2+x^3+... replacing x with (V/R). I'm not sure what to do next, or if this was the right first step to take.

What do you think? I so very much appreciate any help!

Hi Ironhorse! Welcome to MHB! (Smile)

Can it be that your current should be:
$$I = \frac V R \left(1 - e^{-Rt/L}\right)$$
?

The Taylor expansion for $e^x$ is:
$$e^x \approx 1 + x$$
if $x$ is small.
If we substitute that in what I think $I$ should be, we'll get the expression we're supposed to deduce.