Class¶

LCR in series¶

Resonating frequency

$\begin{equation} f_0=\frac{1}{2\pi\sqrt{LC}} \end{equation}$

Quality factor

$\begin{equation} Q=\frac{1}{R}\sqrt{\frac{L}{C}} \end{equation}$

Inductive reactance

$\begin{equation} X_L=2\pi fL \end{equation}$

Capacitive reactance

$\begin{equation} X_C=\frac{1}{2\pi fC} \end{equation}$

Impedance

$\begin{equation} z=\sqrt{(X_L-X_C)^2+R^2} \end{equation}$

Phase angle

$\begin{equation} \phi=\tan^{-1}(\frac{X_L-X_C}{R}) \end{equation}$

In [1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

In [2]:

class lcr():
    def __init__(self,L,C,R,f):
        self.L     = L
        self.C     = C
        self.R     = R
        self.f     = f
        
    def fo(self):
        fr=(2*np.pi*np.sqrt(self.L*self.C))**-1
        return fr
    
    def Q(self):
        ql=np.sqrt(self.L/self.C)/self.R
        return ql
    
    def inductiveReactance(self):
        XL=2*np.pi*self.L*self.f 
        return XL
    
    def capacitiveReactance(self):
        XC=1/(2*np.pi*self.C*self.f)
        return XC
    
    def impedance(self):
        imp=np.sqrt((self.inductiveReactance()-self.capacitiveReactance())**2+self.R**2)
        return imp
    
    def phase(self):
        pi=np.arctan((self.inductiveReactance()-self.capacitiveReactance())/self.R)*180/np.pi
        return pi    # degree
    

In [3]:

l=0.1    #inductance in H
c=1e-6   #capacitance in F
r=10     # resistance in ohm
v=100    #voltage in V

In [4]:

d=lcr(l,c,r,100)
print('Resonating frequency:',d.fo(),'Hz')
print('Q factor:',d.Q())

Resonating frequency: 503.2921210448704 Hz
Q factor: 31.622776601683796

In [5]:

freq=np.arange(10,1500,10)
g=lcr(l,c,r,freq)
xl=g.inductiveReactance()
xc=g.capacitiveReactance()
z=g.impedance()
ph=g.phase()
I=v/z  # current
vr=I*r  #p.d.across reisitor
vl=I*xl  #p.d.across inductor
vc=I*xc  #p.d.across capacitor
power =v*I*np.cos(ph*np.pi/180)

In [6]:

plt.plot(freq,xl,'m.',label='Inductive Reactance')
plt.plot(freq,xc,'c-.',label='Capacitive Reactance')
plt.xlabel(xlabel="Frequency(Hz)",fontsize=14,fontstyle='italic',color="black")
plt.ylabel(ylabel="Reactance(ohm)",fontsize=14,fontstyle='italic',color="black")
plt.title(label="LCR circuit",fontsize=20,fontweight='bold',color="red")
plt.legend()
plt.tight_layout()
plt.savefig("image\LCR1.pdf", dpi = 600) # dpi dot per inch
plt.show()
plt.close()

In [7]:

plt.plot(freq,vr,'g-',label='p.d. across R')
plt.plot(freq,vl,'b-',label='p.d. across L')
plt.plot(freq,vc,'r-',label='p.d. across C')
plt.xlabel(xlabel="Frequency(Hz)",fontsize=14,fontstyle='italic',color="black")
plt.ylabel(ylabel="P.d.(V)",fontsize=14,fontstyle='italic',color="black")
plt.title(label="LCR circuit",fontsize=20,fontweight='bold',color="red")
plt.legend()
plt.tight_layout()
plt.savefig("image\LCR2.pdf", dpi = 600)
plt.show()
plt.close()

In [8]:

plt.plot(freq,z,'m^')
plt.xlabel(xlabel="Frequency(Hz)",fontsize=14,fontstyle='italic',color="black")
plt.ylabel(ylabel="Impedance(ohm)",fontsize=14,fontstyle='italic',color="black")
plt.title(label="LCR circuit",fontsize=20,fontweight='bold',color="red")
plt.tight_layout()
plt.savefig("image\LCR3.pdf", dpi = 600)
plt.show()
plt.close()

In [9]:

plt.plot(freq,I,'c*')
plt.xlabel(xlabel="Frequency(Hz)",fontsize=14,fontstyle='italic',color="black")
plt.ylabel(ylabel="Current(A)",fontsize=14,fontstyle='italic',color="black")
plt.title(label="LCR circuit",fontsize=20,fontweight='bold',color="red")
plt.tight_layout()
plt.savefig("image\LCR4.pdf", dpi = 600)
plt.show()
plt.close()

In [10]:

plt.plot(freq,np.cos(ph*np.pi/180),'k+')
plt.xlabel(xlabel="Frequency(Hz)",fontsize=14,fontstyle='italic',color="black")
plt.ylabel(ylabel="power factor(unitless)",fontsize=14,fontstyle='italic',color="black")
plt.title(label="LCR circuit",fontsize=20,fontweight='bold',color="red")
plt.tight_layout()
plt.savefig("image\LCR7.pdf", dpi = 600)
plt.show()
plt.close()

In [11]:

plt.plot(freq,ph,'k+')
plt.xlabel(xlabel="Frequency(Hz)",fontsize=14,fontstyle='italic',color="black")
plt.ylabel(ylabel="phase angle(degree)",fontsize=14,fontstyle='italic',color="black")
plt.title(label="LCR circuit",fontsize=20,fontweight='bold',color="red")
plt.tight_layout()
plt.savefig("image\LCR5.pdf", dpi = 600)
plt.show()
plt.close()

In [12]:

plt.plot(freq,power,'yo')
plt.xlabel(xlabel="Frequency(Hz)",fontsize=14,fontstyle='italic',color="black")
plt.ylabel(ylabel="Power(W)",fontsize=14,fontstyle='italic',color="black")
plt.title(label="LCR circuit",fontsize=20,fontweight='bold',color="red")
plt.tight_layout()
plt.savefig("image\LCR6.pdf", dpi = 600)
plt.show()
plt.close()

In [13]:

data={}
data.update({'Freqency':freq,'in.rect.':xl,'cap.Rect':xc,'imp.':z,'curren':I,'phase':ph,'power':power})

In [14]:

DF = pd.DataFrame(data)
DF

Out[14]:

	Freqency	in.rect.	cap.Rect	imp.	curren	phase	power
0	10	6.283185	15915.494309	15909.214267	0.006286	-89.963986	0.000395
1	20	12.566371	7957.747155	7945.187077	0.012586	-89.927886	0.001584
2	30	18.849556	5305.164770	5286.324672	0.018917	-89.891615	0.003578
3	40	25.132741	3978.873577	3953.753482	0.025292	-89.855085	0.006397
4	50	31.415927	3183.098862	3151.698800	0.031729	-89.818206	0.010067
...	...	...	...	...	...	...	...
144	1450	911.061870	109.762030	801.362236	0.124788	89.285002	0.155719
145	1460	917.345055	109.010235	808.396673	0.123702	89.291224	0.153021
146	1470	923.628240	108.268669	815.420892	0.122636	89.297330	0.150396
147	1480	929.911425	107.537124	822.435099	0.121590	89.303323	0.147842
148	1490	936.194611	106.815398	829.439497	0.120563	89.309206	0.145355

149 rows × 7 columns

In [15]:

DF.to_csv("data/lcr.csv")  #save data in csv format in excel

In [ ]: