#!/usr/bin/env python
# coding: utf-8

# # INVESTIGATION OF THE ENERGY STORED IN A CAPACITOR
# 
# ## Theory
# The energy stored by a capacitor is given by the equation: $𝑈= 1/2QV$ Given that $𝑄=𝐶V$ then the equation for the energy stored can be written in the form: $𝑈=1/2 CV_{2}$. The capacitor can be charged to various values of $V$ and then the energy stored can be determined by using a Joule meter. 
# 
# The energy stored can be measured as the capacitor discharges. A graph of energy stored against $V^{2}$ should be linear and the value of the capacitance can then be measured.
# 
# 
# ## Apparatus:
# * d.c. power supply
# * Voltmeter (multimeter set on d.c. voltage range or CRO) – resolution ± 0.01V
# * Digital joule meter
# * 4mm leads
# * Suitable switches
# * Electrolytic capacitors e.g. a 1 000 μF or 2 200 μF
# * Resistors e.g. 100 kΩ or other values
# 
# ## Experimental Method:
# 
# ![image.png](attachment:image.png)
# 

# In[1]:


# Importing the necessary libraries
from matplotlib import pyplot as plt
import numpy as np
#from prettytable import PrettyTable

# Preparing the data to be computed and plotted
dt = np.array([
          
    [1.0, 0.15],
    [2.0, 0.29],
    [3.0, 0.38],
    [4.0, 0.50],
    [5.0, 0.60],
    [6.0, 0.81],
    [7.0, 0.90],
    [8.0, 1.13]
])

# Preparing X and y data from the given data
x = dt[:, 0].reshape(dt.shape[0], 1)
X = np.append(x, np.ones((dt.shape[0], 1)), axis=1)
y = dt[:, 1].reshape(dt.shape[0], 1)

# Calculating the parameters using the least square method
theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)

print(f'The parameters of the line: {theta}')

# Now, calculating the y-axis values against x-values according to
# the parameters theta0 and theta1
y_line = X.dot(theta)

# Plotting the data points and the best fit line
plt.scatter(x, y)
plt.plot(x, y_line, 'r')
plt.title('Best fit line using regression method')
plt.xlabel('Length in cm')
plt.ylabel('Resistance')

plt.show()



#def makePrettyTable(table_col1, table_col2):
 #   table = PrettyTable()
  #  table.add_column("Column-1", x)
   # table.add_column("Column-2", Y)
    #return table


# ## Conclusion
# In comparison....
# 

# In[ ]: