[Python] Charging a Capacitor

# -*- coding: utf-8 -*-

# Importing the math module, so we can use eulers e (e^x), written as exp(x) here.
import math

# Importing the pyplot module from matplotlib, so we can plot our findings
import matplotlib.pyplot as plt

# Defining Mega and Micro for easy use on component values
Mega = 10**6
Micro = 10**-6

# Variables for our circuit.
V = 5
C = 1*Micro
R = 100*Mega

# This gives us a time constant of 100 seconds.
# A time constant less than, or equal to 3s will result in a low resolution plot,
# because we only sample one value each second.
T_rc = R*C

# We will use the following formula to calculate the voltage:
# V(t) = V_0 (1-e^(-t/T)), which can be written as
# V(t) = V*(1-e^(-t/R*C)), in our case. T = RC.
# This is stored in V_t.
V_t = []

# A capacitor is 99.9% charged at 5 time constants.
# We want to se it stabilize, so this for loop will find
# values for V_t from 0 to 10 time constants. -> range(1, T_rc.__int__()*10)
for t in range(1, T_rc.__int__()*10):
    # Formula for voltage over a capacitor at a given time, t.
    V_t.append(V*(1-math.exp(-t/(T_rc))))


# Simple plotting of our findings.
plt.plot(V_t)
plt.grid()
plt.xlabel("Time [s]")
plt.ylabel("Current [A]")
plt.show()