CHAPTER 8: INDUCTANCE AND CAPACITANCE MEASUREMENTS

Example 8-1, Page Number: 194

In [20]:
import math

#Variable Declaration

C=0.005*10**-6                     #in farad
Rs=8*10**3                         #in ohm
f=1*10**3                          #in Hz

#Calculations

Xs=1/(2*math.pi*f*C)               #Capacitvie Reactance  in ohm
Rp=(Rs**2+Xs**2)/Rs                #in ohm
Xp=(Rs**2+Xs**2)/Xs                #in ohm
Cp=1/(2*math.pi*f*Xp)              #in farad

#Result

print "Since the measured terminal resistance is 134 kilo ohm, the circuit must consist of a"
print round(Cp*10**6,3),"micro farad capacitor connected in parallel with a",int(Rp/1000),"kilo ohm resistor"
print "For a series connected circuit, the terminal resistance will be much higher than 134 kilo ohm"

Since the measured terminal resistance is 134 kilo ohm, the circuit must consist of a
0.005 micro farad capacitor connected in parallel with a 134 kilo ohm resistor
For a series connected circuit, the terminal resistance will be much higher than 134 kilo ohm

Example 8-2, Page Number: 199

In [13]:
import math

#Variable Declaration
C1=0.1*10**-6                   #in farad

#Calculation

#For R3:R4=100:1
ratio=100.0/1   
Cx=C1*ratio                     #in farad  

print "For R3/R4=100:1, Cx=",round(Cx*10**6),"micro farad"

#For R3:R4=1/100
ratio=1.0/100.0
Cx=C1*ratio                     #in farad 
print "For R3/R4=1:100, Cx=",round(Cx*10**6,3),"micro farad"

For R3/R4=100:1, Cx= 10.0 micro farad
For R3/R4=1:100, Cx= 0.001 micro farad

Example 8-3, Page Number: 202

In [1]:
import math

#Variable Declaration
R3=10*10**3               #in ohm
f=100                     #in Hz
R1=125                    #in ohm
R4=14.7*10**3             #in ohm 
C1=0.4*10**-6             #in farad  

#Calculations 
Cs=C1*R3/R4               #in farad
Rs=R1*R4/R3               #in ohm
D=2*math.pi*f*Cs*Rs       #Dissipation factor  

#Results
print "Cs=",round(Cs*10**6,3),"micro farad"
print "Rs=",round(Rs,1),"ohm"
print "Disspiation factor(D)=",round(D,3)

#****************************Note**********************************************
# The value for C1 as per the problem statement is 0.4 micro farad
#But while calculating,  0.1 micro farad value has been considered  in text book
#C1 is taken to be 0.4 microfarad

Cs= 0.272 micro farad
Rs= 183.8 ohm
Disspiation factor(D)= 0.031

Example 8-4, Page Number: 204

In [28]:
import math

#Variable Declaration

C1=0.1*10**-6                     #in farad
R3=10*10**3                       #in ohm
R1=375*10**3                      #in ohm  
R4=14.7*10**3                     #in ohm
f=100                             #in farad

#Calculations
Cp=C1*R3/R4                       #in farad 
Rp=R1*R4/R3                       #in resistance
D=1/(2*math.pi*f*Cp*Rp)           #Dissipation factor  

#Results
print "Cp=",round(Cp*10**6,3),"micro farad"
print "Rp=",round(Rp/1000,1),"kilo ohm"
print "Dissipation Factor(D)=",'%.2e' % D

Cp= 0.068 micro farad
Rp= 551.3 kilo ohm
Dissipation Factor(D)= 4.24e-02

Example 8-5, Page Number: 204

In [36]:
import math

#Variable Declaration
#From Example 8-3,
Cs=0.068*10**-6              #in farad
Rs=183.8                     #in ohm
f=100                        #in Hz 
R3=10*10**3                  #in ohm
R1=10*10**3                  #in ohm  

#Calculations
Xs=1/(2*math.pi*f*Cs)        #in ohm
Rp=(Rs**2+Xs**2)/Rs          #in ohm  
Xp=(Rs**2+Xs**2)/Xs          #in ohm
Cp=1/(2*math.pi*f*Xp)        #in farad  
R4=C1*R3/Cp                  #in ohm 
R1=R3*Rp/R4                  #in ohm


#Results

print "Rp=",round(Rp*10**-6,2),"mega ohm"
print "Cp=",round(Cp*10**6,3),"micro farad"
print "R4=",round(R4/1000,1),"kilo ohm"
print "R1=",round(R1*10**-6,2),"mega ohm"

Rp= 2.98 mega ohm
Cp= 0.068 micro farad
R4= 14.7 kilo ohm
R1= 2.03 mega ohm

Example 8-6, Page Number: 207

In [39]:
import math

#Variable Declaration

L1=100*10**-3                   #in henry
R4=5*10**3                      #in ohm
Ls=500*10**-3                   #in henry
Rs=270                          #in ohm 

#Calculations
R3=R4*L1/Ls                     #in ohm  
R1=Rs*R3/R4                     #in ohm

#Results
print "R3=",R3/1000,"kilo ohm"
print "R1=",R1,"ohm"

R3= 1.0 kilo ohm
R1= 54.0 ohm

Example 8-7, Page Number: 209

In [41]:
import math

#Variable Declaration
C3=0.1*10**-6                  #in farad
R1=1.26*10**3                  #in ohm
R3=470                         #in ohm
R4=500                         #in ohm
f=100                          #in Hz

#Calculations
Ls=C3*R1*R4                    #in henry 
Rs=R1*R4/R3                    #in ohm 
Q=(2*math.pi*f*Ls)/Rs

#Results

print "Ls=",round(Ls*1000),"mH"
print "Rs=",round(Rs/1000,2),"kilo ohm"
print "Q factor(Q)=",round(Q,2)

Ls= 63.0 mH
Rs= 1.34 kilo ohm
Q factor(Q)= 0.03

Example 8-8, Page Number: 210

In [43]:
import math

#Variable Declaration
C3=0.1*10**-6               #in farad
R1=1.26*10**3               #in ohm
R3=75                       #in ohm
R4=500                      #in ohm
f=100                       #in Hz

#Calculations

Lp=C3*R1*R4                 #in henry 
Rp=R1*R4/R3                 #in ohm
Q=Rp/(2*math.pi*f*Lp)       #Quality factor 

#Results

print "Lp=",round(Lp*1000),"mH"
print "Rp=",round(Rp/1000,2),"kilo ohm"
print "Q factor(Q)=",round(Q)

Lp= 63.0 mH
Rp= 8.4 kilo ohm
Q factor(Q)= 212.0

Example 8-9, Page Number: 211

In [47]:
import math

#Variable Declaration

Lp=63*10**-3                  #in henry
Rp=8.4*10**3                  #in ohm 
f=100                         #in Hz

#Calculations
Xp=2*math.pi*f*Lp             #in ohm            
Rs=Rp*Xp**2/(Xp**2+Rp**2)     #in ohm
Xs=Xp*Rp**2/(Xp**2+Rp**2)     #in ohm
Ls=Xs/(2*math.pi*f)           #in henry

R1=Ls/(C3*R4)                 #in ohm  
R3=R1*R4/Rs                   #in ohm 

#Results

print "Rs=",round(Rs,3),"ohm"
print "Ls=",round(Ls*10**3),"mH"
print "R1=",round(R1/1000,2),"kilo ohm"
print "R3=",round(R3*10**-6,2),"mega ohm"

Rs= 0.187 ohm
Ls= 63.0 mH
R1= 1.26 kilo ohm
R3= 3.38 mega ohm

Example 8-10, Page Number: 214

In [76]:
import math

#Variable Declaration
R1=369.3*10**3                   #in ohm
R3=10*10**3                      #in ohm    
R4=14.66*10**3                   #in ohm 
Rp=553.1*10**3                   #in  ohm
C1=0.1*10**-6                    #in farad 
Cp=0.068*10**-6                  #in farad

#Calcultions
Ceq=round(C1*R3/R4,10)           #Cx+Cp, Equivalent parallel capacitance, in farad
Cx=Ceq-Cp                        #in farad

Req=R1*R4/R3                     #Equivalent resitance in  ohm    

Rx=1/(1/Req-1/Rp)                #in ohm

#Results

print "Cx=",round(Cx*10**12),"pF"
print "Rx=",round(Rx*10**-8,1)*100,"mega ohm"

Cx= 200.0 pF
Rx= 30.0 mega ohm

Example 8-11, Page Number: 221

In [83]:
import math

#Variable Declaration

E=100*10**-3             #in V
R=5                      #in ohm
Xl=100                   #in ohm
Xc=100                   #in ohm

#Calculations
I=E/R                    #At resonance, I is dependent only on R(A)

Vl=I*Xl                  #in V
Vc=I*Xc                  #in V
Q=Vl/E                   #Quality Factor  
print "When R=5 ohm, Xl=100 ohm"
print "Vl=",Vl,"V"
print "Q=",Q
#For the second coil
R=10                     #in ohm 
Xl=100                   #in ohm
Xc=100                   #in ohm  

I=E/R                    #At resonance, I is dependent only on R(A)
Vl=I*Xl                  #in V
Vc=I*Xc                  #in V
Q=Vl/E                   #Quality Factor  

print
print "When R=10 ohm, Xl=100 ohm"
print "V=",Vl
print "Q=",Q

When R=5 ohm, Xl=100 ohm
Vl= 2.0 V
Q= 20.0

When R=10 ohm, Xl=100 ohm
V= 1.0
Q= 10.0

Exanoke 8-12, Page Number: 225

In [93]:
import math

#Variable Declaration

C=147*10**-12                  #in farad
f=1.25*10**6                   #in Hz
Q=98.0                         #Q Factor

#Calculations 
L=1/(C*(2*math.pi*f)**2)       #in henry     
R=(2*math.pi*f*L)/Q            #in ohm

#Results
print "L=",round(L*10**6),"micro henry"
print "R=",round(R,1),"ohm"

L= 110.0 micro henry
R= 8.8 ohm