Problem #$1$

You are told that the discharge current $i$ of a series $RC$ circuit varies with time according to this

function:

$i(t)=5e^{-\frac{t}{}}$

Note: $t$ is time, $($tau$)$ is some fixed value $($in seconds$)$ that is characteristic of this $RC$ circuit.

Assume the initial starting time is $t=0$ seconds, and the current is measured in amperes $($A$).$

a$)$ Look up$"$ the phrase "capacitor discharge" for a series $RC$ circuit. From your research, what

does the $$ in the equation above represent, and why is it important?

b$)$ What is the maximum amount of current in this circuit?

c$)$ Using the discharge equation, determine how many time constants are needed for the current

to drop to $250mA.$

d$)$ Write a Python script to plot the current i versus the unit$-$less ratio $,$ where $=\frac{t}{}.$ In other

words, you are plotting $i()$ versus $.$ The graph should have these properties:

$$ ranges from $0$ to $10.$ Choose a reasonable step size to get a smooth curve.

On the same graph, plot a horizontal dashed line that passes through the $250mA$ level.

Label the axes and provide a title.

For the $x-$axis label, make it fancier by displaying the actual Greek symbol for

alpha, i$.$e$.,.$

Note: Include an image of the output graph with your document.

Save the script using this file name: hw$1\_$p$1.$py$.$ PLEASE PROVIDE FULL PYTHON CODE, AND ANSWER THE QUESTIONS. WILL THUMBS UP IF BOTH PROVIDED