Chapter2:AC CIRCUITS¶

Ex2.1:pg-147¶

In [4]:
t=3*10**-3;                  #Assigning values to parameters
w=314;
Im=141.4*sin(math.pi/2);
f=w/(2*math.pi);
T=1/f;
t=3*(10**-3);
i=141.4*sin(w*t);
print"Maximum value of current",round(Im,2),"A"
print"Frequency",round(f,1),"HZ"
print"Time period",round(T,2),"sec"
print"Instantaneous value of current at t=3 msec",round(i,2),"A"

Maximum value of current 141.4 A
Frequency 50.0 HZ
Time period 0.02 sec
Instantaneous value of current at t=3 msec 114.36 A


Ex2.2:pg-147¶

In [8]:
f=60.0;               #Assigning values to parameters
Im=12.0;
i=Im*sin(377/360)
print"Current at t=1/360 sec",round(i,2),"A"
i1=9.6;
t=math.asin(i1/Im)/377;
print"Time taken to reach i1",round(t,5),"sec"

Current at t=1/360 sec 10.1 A
Time taken to reach i1 0.00246 sec


Ex2.3:pg-148¶

In [1]:
w=942.0;            #Assigning values to parameters
Vm=10.0;
V=6.0;
t=math.asin(V/Vm)/w;
f=w/(2*math.pi);
T=1.0/f;
t2=t+T;
print"Time taken to reach 6V second time=",round(t2*1000,2),"msec"

Time taken to reach 6V second time= 7.35 msec


Ex2.4:pg-150¶

In [25]:
from scipy import integrate
import math
V1=V[0]
Vavg=V1/(2*math.pi)
print"the average value of voltage is Vavg=",round(Vavg,3),"volts"

the average value of voltage is Vavg= 6.366 volts


Ex2.5:pg-152¶

In [5]:
from scipy import integrate
#y=10*t,the current equation
T=4;
Res=Res[0]/T
print"Average current value",round(Res,2),"A"

Average current value 5.0 A


Ex2.6:pg-153¶

In [4]:
from scipy import integrate
#y=6*t,the voltage equation
T=3;
Res=Res[0]/T
print"Average voltage value is Res=",round(Res,2),"Volts"

Average voltage value is Res= 9.0 Volts


Ex2.7:pg-153¶

In [22]:
from scipy import integrate
Vm=1;   #Assuming Vm=1
#y=Vm*sin(t),the voltage Equation
#y1=0.866*Vm*sin(t)
T=math.pi;
Res1=Res1[0]
Res2=Res2[0]
Res3=Res3[0]
Res=(Res1+Res2+Res3)/T
print"Average voltage value",round(Res,2),"volts"

Average voltage value 0.62 volts


Ex2.8:pg-155¶

In [20]:
from scipy import integrate
Vm=1;  #Assuming Vm=1;
#y=Vm*sin(t)  #Defining voltage equation
T=math.pi;
Res=Res[0]/T
print"Average voltage value",round(Res,3),"Volts"

Average voltage value 0.594 Volts


Ex2.10:pg-159¶

In [19]:
from scipy import integrate
Vm=1;        #Assuming Vm=1
#y=Vm*Vm*sin(t)*sin(t), #Defining Voltage Equation
T=2*math.pi;
Res=sqrt(Res[0]/T)
print"Rms value of voltage",round(Res,2),"Volts"

Rms value of voltage 0.56 Volts


Ex2.11:pg-160¶

In [24]:
from scipy import integrate
Vm=1;            #Assuming Vm=1
#y=Vm*Vm*sin(t)*sin(t)     #Defining Voltage Equation
T=2*math.pi;
Res=sqrt(Res[0]/T)
print"Rms value of voltage",round(Res,3),"Volts"

Rms value of voltage 0.477 Volts


Ex2.12:pg-161¶

In [28]:
from scipy import integrate
Vm=1;  #Assuming Vm=1
#y=Vm*Vm*sin(t)*sin(t),Defining Voltage Equation
#y1=0.866*0.866*Vm*Vm*sin(t)*sin(t)
T=math.pi;
VRms=sqrt((Res1[0]+Res2[0]+Res3[0])/T)
print"Rms voltage value is=",round(VRms,3),"Volts"

Rms voltage value is= 0.68 Volts


Ex2.13:pg-163¶

In [29]:
from scipy import integrate
Vm=1;          #Assuming Vm=1
#y=10*t*10*t, Defining Current Equation
T=4;
Irms=sqrt(Res[0]/T)
print"Rms current value is Irms=",round(Irms,2),"A"

Rms current value is Irms= 8.16 A


Ex2.14:pg-164¶

In [31]:
from scipy import integrate
Vm=1;              #Assuming Vm=1
#y=sin(t)*sin(t),Defining Voltage Equation
T=math.pi;
Res=sqrt(Res[0]/T)
print"Rms voltage value",round(Res,3),"volts"

Rms voltage value 0.697 volts


Ex2.15:pg-165¶

In [34]:
from scipy import integrate
Vm=1;             #Assuming Vm=1
#y=sin(t+(math.pi/3))*sin(t+(math.pi/3)),Defining Voltage Equation
T=2*(math.pi/3);
Res=sqrt(Res[0]/T)
print"Rms voltage value",round(Res,4),"volts"

Rms voltage value 0.7768 volts


Ex2.16:pg-167¶

In [35]:
from scipy import integrate
#y=(10+10*sin(t))*(10+10*sin(t)),Defining Current Equation
T=2*math.pi;
Res=sqrt(Res[0]/T)
print"Rms current value",round(Res,2),"A"

Rms current value 12.25 A


Ex2.17:pg-168¶

In [37]:
Im=62.35;
w=323;
#y=Im*sin(w*t), Defining Voltage Equation
fr=w/(2*math.pi);
Irms=Im/sqrt(2);
Iavg=0.637*Im;
formfac=Irms/Iavg;
print"Maximum value of current",round(Im,2),"A"
print"Frequency",round(fr,2),"Hertz"
print"Rms value of current",round(Irms,1),"A"
print"Average value of current",round(Iavg,1),"A"
print"Form factor",round(formfac,2)

Maximum value of current 62.35 A
Frequency 51.41 Hertz
Rms value of current 44.1 A
Average value of current 39.7 A
Form factor 1.11


Ex2.19:pg-175¶

In [38]:
import cmath
V1=42.43+1j*0;              #Defining voltage equations in rectangular form
V2=14.14+1j*24.49;
Va=V1+V2;
[Ro,Theta]=cmath.polar(Va);
Vm=Ro*sqrt(2);
print"Maximum value of voltage considering addition of voltages",round(Vm,2),"Volts"
#function, y=Ro*sin(t+Theta),Defining voltage equation
Vb=V1-V2;
[Ro1,Theta1]=cmath.polar(Vb);
Vm1=Ro1*sqrt(2);
#function y1=f(t),y1=Ro*sin(t+Theta1),Defining voltage equation
print"Maximum value of voltage considering difference of voltages",round(Vm1,2),"Volts"

Maximum value of voltage considering addition of voltages 87.18 Volts
Maximum value of voltage considering difference of voltages 52.92 Volts


Ex2.21:pg-177¶

In [54]:
import cmath
V1=17.68             #Defining voltage equations in rectangular form
V2=6.12+1j*3.54
V3=1j*21.21
V4=10-1j*10;
V=V1+V2+V3+V4;
[Ro,Theta]=cmath.polar(V);
Vm=Ro*sqrt(2)
t1=math.degrees(Theta)
#function y=f(t), y=Ro*sqrt(2)*sin(t+Theta), endfunction
print"Maximum Voltage value",round(Vm,2),"Volts"
print"the value of Theta is=",round(t1,2),"degrees"

Maximum Voltage value 52.15 Volts
the value of Theta is= 23.58 degrees


Ex2.22:pg-178¶

In [46]:
import cmath
V1=36.75+1j*21.22             #Defining voltage equations in rectangular form
V2=-45.93-1j*26.52
V3=-50+1j*50;
V=-30.59+1j*94.15;
V4=V-(V1+V2+V3);
[Ro,Theta]=cmath.polar(V4);
t=math.degrees(Theta)
#function y=f(t), y=Ro*sqrt(2)*sin(t+Theta), endfunction
V=Ro*sqrt(2)
print"Maximum Voltage value is=",round(V,2),"Volts"
print"the vlaue of Theta is=",round(t,2),"degrees"

Maximum Voltage value is= 80.78 Volts
the vlaue of Theta is= 59.97 degrees


Ex2.23:pg-179¶

In [55]:
import cmath
I1=2.12+1j*3.67             #Defining current equations in rectangular form
I2=-3.07+1j*1.77
I3=-1.84+1j*1.06;
I4=-(I1+I2+I3);
[Ro,Theta]=cmath.polar(I4);
#function y=f(t), y=Ro*sqrt(2)*sin(t+Theta), endfunction
I=Ro*sqrt(2)
t=math.degrees(Theta)
print"Maximum current value is I=",round(I,2),"A"
print"the value of Theta is t=",round(t,2),"degrees"

Maximum current value is I= 10.0 A
the value of Theta is t= -66.77 degrees


Ex2.24:pg-181¶

In [59]:
V1=230            #Defining voltage equations in rectangular form
V2=-115+1j*200;
V3=-115-1j*200;
V=V1+V2+V3;
[Ro,Theta]=cmath.polar(V);
#function y=f(t), y=Ro*sqrt(2)*sin(t+Theta), endfunction
ER=Ro*sqrt(2)

print"Maximum Voltage value is ER=",round(ER,2),"Volts"

Maximum Voltage value is ER= 0.0 Volts


Ex2.25:pg-181¶

In [60]:
V1=70.71             #Defining voltage equations in rectangular form
V2=1j*176.78
V3=91.86+1j*53.04
V4=100-1j*100;
V=V1+V2+V3+V4;
[Ro,Theta]=cmath.polar(V);
#function y=f(t), y=Ro*sqrt(2)*sin(t+Theta), endfunction
V=Ro*sqrt(2)
print"Maximum Voltage value with V2 polarity as it is",round(V,2),"Volts"
V=V1-V2+V3+V4;
[Ro1,Theta1]=cmath.polar(V);
#function y1=f(t), y1=Ro1*sqrt(2)*sin(t+Theta), endfunction
V=Ro1*sqrt(2)
print"Maximum Voltage value with polarity of V2 reversed",round(V,2),"Volts"

Maximum Voltage value with V2 polarity as it is 414.24 Volts
Maximum Voltage value with polarity of V2 reversed 487.86 Volts


Ex2.26:pg-190¶

In [1]:
C=318*10**-6;         #Assignig values to parameters
V=230.0;
f=50.0;
Xc=1.0/(2*math.pi*f*C);
I=V/Xc;
Vm=sqrt(2)*V;
Im=sqrt(2)*I;
#function y=f(t), y=Vm*sin(2*%pi*f*t),endfunction
#function y1=f(t), y1=Im*sin(2*%pi*f*t+%pi/2),endfunction
print"Peak voltage value",round(Vm,2),"Volts"
print"Peak currnet value",round(Im,2),"A"

Peak voltage value 325.27 Volts
Peak currnet value 32.5 A


Ex2.27:pg-190¶

In [1]:
L=10*10**-3;             #ASssigning values to parameters
Im=5;
w=2000;
#function y=f(t), y=Im*sin(w*t+%pi/2),endfunction
I=Im/sqrt(2);
Xl=2*math.pi*L;
Vm=L*Im*w;
Vl=Vm/sqrt(2);
print"Voltage Vl",round(Vl,2),"Volts"

Voltage Vl 70.71 Volts


Ex2.28:pg-191¶

In [5]:
V=150;               #Assigning values to parameters
f=50;
L=0.2;
Xl=2*math.pi*f*L;
Vm=V*sqrt(2);
I=V/Xl;
Im=sqrt(2)*I;
#function y=f(t), y=Vm*sin(2*%pi*f*t),endfunction
#function y1=f(t), y1=Im*sin(2*%pi*f*t-(%pi/2)) endfunction
print"Maximum voltage value",round(Vm,2),"Volts"
print"Maximum current value",round(Im,2),"A"

Maximum voltage value 212.13 Volts
Maximum current value 3.38 A


Ex2.29:pg-202¶

In [28]:
import math
R=7.0;             #Assigning values to parametrs
L=31.8*10**-3;
V=230.0;
f=50.0;
Xl=2*math.pi*f*L;
Xl=round(Xl);
Zcoil=sqrt(R*R+Xl*Xl);
I=V/Zcoil;
Phi=math.atan(Xl/R);
Phi1=math.degrees(Phi)
PF=cos(Phi)
I=round(I,2);
P=V*I*0.574;
print"Circuit Current=",round(I,2),"A"
print"Phase angle=",round(Phi1),"degrees"
print"Power factor=",round(PF,2)
print"Power consumed=",round(P,2),"Watts"

Circuit Current= 18.84 A
Phase angle= 55.0 degrees
Power factor= 0.57
Power consumed= 2487.26 Watts


Ex2.30:pg-203¶

In [1]:
import cmath
V=200.0;                #Assigning values to parameters
R=20.0;
f=50.0;
L=0.1;
Xl=2*math.pi*f*L;
C=50*10**-6;
Xc=1.0/(2*math.pi*f*C);
X=Xc-Xl;
Z=R-1j*X;
[Ro,theta]=cmath.polar(Z)
I=V/Ro;
PF=cos(theta);
PF=round(PF,3);
I=round(I,2);
PA=V*I*PF;
PR=V*I*sin(theta);
P=V*I;
print"Circuit Current=",round(I,2),"A"
print"Circuit Impedance=",round(Ro,2),"ohms"
print"Power Factor=",round(PF,3)
print"Active Power=",round(PA,2),"Watts"
print"Reactive Power=",round(PR,1),"VAR"
print"Apparen Power=",round(P),"VA"

Circuit Current= 5.27 A
Circuit Impedance= 37.94 ohms
Power Factor= 0.527
Active Power= 555.46 Watts
Reactive Power= -895.7 VAR
Apparen Power= 1054.0 VA


Ex2.31:pg-204¶

In [37]:
import cmath
V=200+1j*0;             #Assigning values to parameters
R1=10;
R2=20;
R=R1+R2;
L1=0.05;
L2=0.1;
f=50;
Xl1=2*math.pi*f*L1;
Xl2=2*math.pi*f*L2;
Xl=Xl1+Xl2;
C=50*10**-6;
Xc=1/(2*math.pi*f*C);
X=Xc-Xl;
Z=R-1j*X;
[Ro,theta]=cmath.polar(Z);
I=V/Z;
Z1=R1+1j*Xl1;
Z2=R2-1j*(Xc-Xl2)
[Ro1,Theta1]=cmath.polar(Z1);
[Ro2,Theta2]=cmath.polar(Z2);
[ro,th]=cmath.polar(I);
V1=ro*Ro1;
V2=ro*Ro2;
print"Circuit Current",round(ro,2),"A"
print"Voltage V1",round(V1,1),"Volts"
print"Voltage V2",round(V2,1),"Volts"

Circuit Current 5.84 A
Voltage V1 108.7 Volts
Voltage V2 221.5 Volts


Ex2.32:pg-205¶

In [2]:
import cmath
V=100+0*1j;                     #Assignig values to parametrs
Z1=17.32+10*1j;
V1=34.64-20*1j;
V2=V-V1;
[Ro,Theta]=cmath.polar(V2);
[ro,theta]=cmath.polar(Z1);
[r,t]=cmath.polar(V1);
I=Ro/r;
[ro1,t1]=cmath.polar(I);
I=round(I);
Z2=V2/I;
[r1,t1]=cmath.polar(Z2);
print"Impedance Z2","=",Z2,"=",cmath.polar(Z2),"=",round(r1,3),"ohms"
# The answer in the book is wrong ,The value of I is wrong in the book.

Impedance Z2 = (32.68+10j) = (34.17575748977629, 0.2969500127663617) = 34.176 ohms


Ex2.33:pg-206¶

In [82]:
import cmath
V=150+180*1j;          #Assigning values to parameters
I=5-4*1j;
Z=V/I;
print"Impedance =",Z,"=",round(Z.imag,1),"ohms"
[Ro,Theta]=cmath.polar(Z);
P=V*I*cos(Theta);
[r,t]=cmath.polar(P);
print"Power consumed =",round(r,4),"Watts"

Impedance = (0.731707317073+36.5853658537j) = 36.6 ohms
Power consumed = 30.0 Watts


Ex2.34:pg-206¶

In [4]:
import cmath
V=127.28+1j*0;             #Assigning values to parameters
I=1.251-1j*1.251
Z=V/I
[r1,t1]=cmath.polar(Z);
[Ro,Theta]=cmath.polar(I)
P=V*I*cos(Theta)
[r,t]=cmath.polar(P)
print"Resistive and reactive part of impedance =",Z,"=",cmath.polar(Z),"=",round(r1,3),"ohms"
print"Average Power taken=",round(r,2),"Watts"

Resistive and reactive part of impedance = (50.8713029576+50.8713029576j) = (71.9428865782764, 0.7853981633974483) = 71.943 ohms
Average Power taken= 159.23 Watts


Ex2.35:pg-207¶

In [5]:
Z1=12.5+1j*21;          #Assigning values to parameters
V=50+1j*0;
I1=V.real/Z1.real;
I2=0.722-0.723*1j;
Z=V/I2;
Z2=Z-Z1;
[r,t]=cmath.polar(Z2);
print"Impedance Z2 =",Z2,"=",cmath.polar(Z2),"=",round(r,3),"ohms"

Impedance Z2 = (22.0781134909+13.6260056149j) = (25.944385217897505, 0.5529507762186462) = 25.944 ohms


Ex2.40:pg-212¶

In [6]:
#function v=f(t), v=200*sin(377*t), endfunction         #Defining functions
#function i=f1(t), i=8*sin(377*t-%pi/6), endfunction
V=200.0/sqrt(2);#Assigning values to parameters
V=round(V,2);
I=8.0/sqrt(2);
I=round(I,2);
P=V*I*cos(math.pi/6)
print"Active Power=",round(P,3),"Watts"
Q=V*I*sin(math.pi/6);
print"Reactive Power=",round(Q,2),"VAR"
S=V*I;
print"Apparent Power=",round(S,2),"Watts"

Active Power= 693.199 Watts
Reactive Power= 400.22 VAR
Apparent Power= 800.44 Watts


Ex2.43:pg-215¶

In [7]:
import cmath
#function i=f(t), i=5*sin(314*t+2*%pi/3), endfunction;   #Defining functions
#function v=f1(t), v=20*sin(314*t+5*%pi/6), endfunction;
I=-1.77+3.065*1j;
V=-12.24+7.07*1j;
Z=V/I;
[r,t]=cmath.polar(Z);
P=V*I*cos(t);
[ro,theta]=cmath.polar(P);
print"Impedance =",Z,"=",round(Z.real,3),"ohms"
print"Average Power =",round(ro,2),"Watts"

Impedance = (3.45924144606+1.99580510293j) = 3.459 ohms
Average Power = 43.33 Watts


Ex2.45:pg-216¶

In [3]:
import cmath
import numpy as np
from numpy.linalg import inv
f=50.0;
I=5.0;
V=250.0;
I1=5.8
Z=V/I;
A=[1, (1/(2*math.pi*50))**2],[1, (1/(2*math.pi*60))**2]
B=[50**2],[43.1**2];
res=np.dot(inv(A),B);
r=res[0][0];
P=I1**2*(sqrt(r));
print"Power absorbed =",round(P,1),"Watts"

Power absorbed = 670.8 Watts


Ex2.46:pg-218¶

In [8]:
#function vl=f(t), vl=300*sin(1000*t), endfunction;    #Defining functions
R=20.0;          #Assigning values to parameters
w=1000;
Z=R/cos(math.pi/4);
Xc=sqrt(Z*Z-R*R);
Xl=2*Xc;
L=Xl/w;
C=1.0/(w*Xc);
print"Inductance Value=",round(L,2),"Henery"

Inductance Value= 0.04 Henery
Capacitance Value= 5e-05 farad


Ex2.47:pg-219¶

In [9]:
import cmath
Vr=10;         #Assigning values to parameters
Vl=15;
Vc=10;
V=sqrt(Vr^2+(Vl-Vc)^2);
V=10+1j*0+0+1j*15+0-1j*10;
[r,t]=cmath.polar(V);
print"Voltage=",round(r,2),"Volts"

Voltage= 11.18 Volts


Ex2.48:pg-219¶

In [10]:
import cmath
L=0.01;         #Assigning value sto parameters
fr=50;
#function v=f(t), y=400*sin(3000*t-10),endfunction;   #Defining functions
#function i=f1(t),i=10*sqrt(2)*cos(3000*t-55), endfunction;
V=278.54-1j*49.11;
I=8.191+5.7*1j;
Z=V/I;
[r,t]=cmath.polar(Z);
Xl=3000*L;
Xc=50;
C=1.0/(2*math.pi*fr*Xc);
print"impedence Z=",Z,"=",cmath.polar(Z),"=",round(r,2),"ohms"

impedence Z= (20.0998621434-19.9828121374j) = (28.342851640290757, -0.7824779572137082) = 28.34 ohms
Capacitance C= 6e-05 farad


Ex2.49:pg-221¶

In [11]:
Vr=25;              #Assigning values to parameters
Vcoil=40;
Vc=55;
Vrcoil=50;
I=0.345;
C=20*10**-6;
Xc=Vc/I;
f=1/(2*math.pi*C*Xc);
R=Vr/I;
Zcoil=Vcoil/I;
Zrcoil=Vrcoil/I;
r=(Zrcoil**2-(R**2+Zcoil**2))/(2*R);
Xl=sqrt(Zcoil**2-r**2);
Z=sqrt((R+r)**2+(Xc-Xl)**2);
I=round(I,3);
Z=round(Z);
V=I*Z;
print"Voltage=",round(V,3),"Volts"
#The answer in the book is wrong,which is 35.046

Voltage= 34.155 Volts


Ex2.50:pg-227¶

In [12]:
R=10.0;               #Assigning values to parameters
L=0.014;
C=100*10**-6;
wr=1.0/sqrt(L*C);
Q=(1.0/R)*(sqrt(L/C));
BW=R/L;
w1=wr-BW/2;
w2=wr+BW/2;
Vm=1;
V=1/sqrt(2);
Vc=(V/R)*sqrt(L/C);
print"Quality factor=",round(Q,3)
print"Maximum value of voltage across capacitor=",round(Vc,3),"Volts"

Resonant frequency= 845.15 rad/sec
Quality factor= 1.183
Lower frequency= 488.0 rad/sec
Upper frequency= 1202.3 rad/sec
Maximum value of voltage across capacitor= 0.837 Volts


Ex2.51:pg-228¶

In [13]:
V=10/sqrt(2);         #Assigning values to parameters
Vc=500;
BW=400/(2*math.pi);
R=100;
Q=Vc/V;
BW=round(BW,2);
Q=round(Q,2);
fr1=(Q*BW);
f1=fr1-(BW/2);
f2=fr1+BW/2;
L=R/(2*math.pi*BW);
fr=1.0/(2*math.pi*sqrt(L*C));
C=1.0/(fr1*fr1*4*math.pi*math.pi*L);
print"Resonant frequency=",round(fr1,2),"Hertz"
print"Lower frequency=",round(f1,2),"Hertz"
print"Upper frequency=",round(f2,2),"Hertz"
print"Inductor value=",round(L,2),"Hertz"
# the answer of the capacitance in ths book is given in nF

Resonant frequency= 4501.4 Hertz
Lower frequency= 4469.57 Hertz
Upper frequency= 4533.23 Hertz
Inductor value= 0.25 Hertz
Capacitor value= 5e-09 Farads


Ex2.52:pg-229¶

In [14]:
f=1*10**6;              #Assigning values to parameters
C1=500*10**-12;
C2=600810**-12;
Xl=1.0/(2*math.pi*f*C1);
L=Xl/(2*math.pi*f);
R=30.623;
Q=(1/R)*sqrt(L/C1);
print"Resistance=",round(R,2),"ohms"
print"Inductance=",round(L,9),"Henery"
print"Quality Factor=",round(Q,2)

Resistance= 30.62 ohms
Inductance= 5.0661e-05 Henery
Quality Factor= 10.39


Ex2.53:pg-230¶

In [151]:
r=2.0;                  #Assigning values to parameters
L=0.01
V=230.0;
f=50.0;
C=1.0/(f*f*4*math.pi*math.pi*L);
Ir=V/r;
Vc=(V/r)*sqrt(L/C);
print"Current across capacitor C=","{:.3e}".format(C),"Farad"
print"Current I=",round(Ir,2),"A"
print"Voltage across the capacitor Vc=",round(Vc,1),"Volts"

Current across capacitor C= 1.013e-03 Farad
Current I= 115.0 A
Voltage across the capacitor Vc= 361.3 Volts


Ex2.54:pg-230¶

In [6]:
L=0.1;                   #Assigning values to parameters
R=10.0;
V=230.0;
f=50.0;
C=200*10**-6;
Xl=2*math.pi*f*L;
Xc=1.0/(2*math.pi*f*C);
Z=sqrt(R*R+(Xl-Xc)*(Xl-Xc));
I=V/Z;
Zcoil=sqrt(R*R+Xl*Xl);
Vcoil=I*Zcoil;
Vc=I*Xc;
print"Circuit Current I=",round(I,2),"Amperes"
print"Coil impedance Zcoil=",round(Zcoil,2),"Ohms"
print"Volts","Coil voltage Vcoil=",round(Vcoil,1),"Volts"
print"Capacitor Voltage Vc=",round(Vc,2),"Volts"
fr=1.0/(2*math.pi*sqrt(L*C));
Ir=V/R;
Xl=2*math.pi*fr*L;
Xc=Xl;
Zcoil=sqrt(R*R+Xl*Xl);
Vcoil=Ir*Zcoil;
Vc=Ir*Xc;
print"Circuit Current at resonance Ir=",round(Ir,2),"Amperes"
print"Coil impedance at resonance Zcoil=",round(Zcoil,2),"Ohms"
print"Coil voltage at resonance Vcoil=",round(Vcoil,3),"Volts"
print"Capacitor Voltage at resonance Vc=",round(Vc,2),"Volts"

Circuit Current I= 12.47 Amperes
Coil impedance Zcoil= 32.97 Ohms
Volts Coil voltage Vcoil= 411.1 Volts
Capacitor Voltage Vc= 198.45 Volts
Circuit Current at resonance Ir= 23.0 Amperes
Coil impedance at resonance Zcoil= 24.49 Ohms
Coil voltage at resonance Vcoil= 563.383 Volts
Capacitor Voltage at resonance Vc= 514.3 Volts


Ex2.55:pg-232¶

In [15]:
Vr=200.0;           #Assiging values to parameters
P=15.3;
fr=10000.0;
BW=1000.0;
R=Vr**2/P;
Q=fr/BW;
L=Q*R/(2*math.pi*fr);
C=1.0/(4*math.pi*math.pi*fr*fr*L);
print"resistance=",round(R,2),"ohms"
print"inductor=",round(L,3),"Henery"
#The answer of the capacitance in the book is given in the form of pF

resistance= 2614.38 ohms
inductor= 0.416 Henery


Ex2.56:pg-236¶

In [15]:
R=20.0;             #Assigning values to parameters
L=31.8*10**-3;
V=230.0;
f=50.0;
I1=V/R;
Xl=2*math.pi*f*L;
I2=V/Xl;
I2=round(I2);
I=sqrt(I1*I1+I2*I2);
pf=I1/I;
pf=round(pf,3);
P=V*I*pf;
print"Line current=",round(I,2),"A"
print"Power factor=",round(pf,3)
print"Power consumed=",round(P,1),"Watts"

Line current= 25.71 A
Power factor= 0.447
Power consumed= 2643.7 Watts


Ex2.57:pg-238¶

In [19]:
import cmath
V=230+1j*0;            #Assigning values to parameters
L=10*10**-3;
f=50.0;
R=10.0;
Xl=2*math.pi*f*L;
Xc=1.0/(2*math.pi*f*C);
Z1=10+1j*3.14;
Z2=10-1j*6.37;
Z=(Z1*Z2)/(Z1+Z2);
I=V/Z;
I1=V/Z1;
[r1,t1]=cmath.polar(I1);
I2=V/Z2;
[r2,t2]=cmath.polar(I2);
[r,t]=cmath.polar(Z1);
[ro,th]=cmath.polar(Z2);
[rot,tt]=cmath.polar(Z);
pf1=cos(t);
pf2=cos(th);
pft=cos(tt);
P1=I1*I1*R;
[r4,t4]=cmath.polar(P1);
P2=I2*I2*R;
[r5,t5]=cmath.polar(P2);
print"Total Impedance=",round(Z.real,2),"Ohms"
print"Branch current I1=",I1,"=",cmath.polar(I1),"=",round(r1,2),"Amperes"
print"Branch current I2=",I2,"=",cmath.polar(I2),"=",round(r2,3),"Amperes"
print" Power factor of branch1=",round(pf1,3)
print" Power factor of branch2=",round(pf2,3)
print" Total Power factor=",round(pft,3)
print" Power consumed by branch 1=",P1,"=",cmath.polar(P1),"=",round(r4,2),"Watts"
print" Power consumed by branch 2=",P2,"=",cmath.polar(P2),"=",round(r5,2),"Watts"
#In the book the answer is given in the polar form.

Total Impedance= 6.1 Ohms
Branch current I1= (20.935812619-6.57384516237j) = (21.94364806128091, -0.3042508322379845) = 21.94 Amperes
Branch current I2= (16.3611517966+10.4220536945j) = (19.3986208613536, 0.5671820281530153) = 19.399 Amperes
Power factor of branch1= 0.954
Power factor of branch2= 0.843
Total Power factor= 0.995
Power consumed by branch 1= (3950.928098-2752.57581012j) = (4815.236902373575, -0.608501664475969) = 4815.24 Watts
Power consumed by branch 2= (1590.68084902+3410.33605055j) = (3763.0649132254307, 1.1343640563060304) = 3763.06 Watts


Ex2.58:pg-239¶

In [42]:
import cmath
Vm=100.0;         #Assigning values to parameters
w=3.0;
#function v=f(t), v=Vm*sin(w*t), endfunction   #Defining voltage equation
V=Vm/sqrt(2)+0*1j;
L=1.0/3;
Xl=w*L;
C=1.0/6;
Xc=1.0/(w*C);
Z1=1+1j*1;
Z2=1-1j*2;
I1=V/Z1;
[r,t]=cmath.polar(I1);
I2=V/Z2;
[r1,t1]=cmath.polar(I2);
I=I1+I2;
[r2,t2]=cmath.polar(I);
print"Branch current I1=",I1,"=",cmath.polar(I1),"=",round(r,3),"A"
print"Branch current I2=",I2,"=",cmath.polar(I2),"=",round(r1,3),"A"
print"Total current=",I,"=",cmath.polar(I),"=",round(r2,3),"A"
#In the book the final answer is given in the polar form.

Branch current I1= (35.3553390593-35.3553390593j) = (49.99999999999999, -0.7853981633974483) = 50.0 A
Branch current I2= (14.1421356237+28.2842712475j) = (31.622776601683785, 1.1071487177940904) = 31.623 A
Total current= (49.4974746831-7.07106781187j) = (49.999999999999986, -0.14189705460416396) = 50.0 A


Ex2.59:pg-240¶

In [41]:
import cmath
Z1=10+1j*15;         #Assigning values to parameters
Z2=6-1j*8;
I=15.0;
Z=(Z1*Z2)/(Z1+Z2);
V=I*Z;
I1=V/Z1;
I2=V/Z2;
P1=I1**2*real(Z1);
[r,t]=cmath.polar(P1);
P2=I2**2*real(Z2);
[r1,t1]=cmath.polar(P2);
print"Power taken by branch 1=",P1,"=",cmath.polar(P1),"=",round(r,3),"Watts"
print"Power taken by branch 2=",P2,"=",cmath.polar(P2),"=",round(r1,3),"Watts"
#In the book the final answer is given in the polar form.

Power taken by branch 1= (-660.306369256-328.943832303j) = (737.7049180327872, -2.679411319197999) = 737.705 Watts
Power taken by branch 2= (599.717817791+1307.5517334j) = (1438.5245901639341, 1.1407665632998834) = 1438.525 Watts


Ex2.60:pg-241¶

In [40]:
V=200;       #Assigning values to parameters
f=50;
Ra=10;
La=0.12;
Rb=20;
Cb=40*10**-6;
Xla=2*math.pi*f*La;
Xcb=1/(2*math.pi*f*Cb);
Za=Ra+1j*Xla;
Zb=Rb-1j*Xcb;
Zeq=(Za*Zb)/(Za+Zb);
[r,t]=cmath.polar(Zeq);
Ia=V/Za;
[r1,t1]=cmath.polar(Ia);
Ib=V/Zb;
[r2,t2]=cmath.polar(Ib);
pf=cos(t);
print"Branch current 1=",Ia,"=",cmath.polar(Ia),"=",round(r1,3),"A"
print"Branch current 2=",Ib,"=",cmath.polar(Ib),"=",round(r2,3),"A"
print"power factor=",round(pf,2)
#In the book the final answer is given in the polar form.

Branch current 1= (1.31473160452-4.95642138023j) = (5.127829179131076, -1.3115093180978645) = 5.128 A
Branch current 2= (0.594126408901+2.36395386995j) = (2.437470838597086, 1.3245687251899845) = 2.437 A
power factor= 0.59


Ex2.61:pg-242¶

In [36]:
Z1=14.14-1j*14.14;            #Assigning values to parameters
Z2=26+1j*15;
I=10;
Zeq=Z1+Z2;
V=I*Zeq;
Zeq=(Z1*Z2)/(Z1+Z2);
I=V/Zeq;
[r,t]=cmath.polar(I);
print"Supply current=",I,"=",cmath.polar(I),"=",round(r,3),"A"
#In the book the final answer is given in the polar form.

Supply current= (25.6159787883+8.06347214395j) = (26.855128975653326, 0.3049633114846056) = 26.855 A


Ex2.62:pg-243¶

In [32]:
I=25*1j;           #Assigning values to parameters
Z1=3-1j*4;
Z2=10;
I1=I*Z2/(Z1+Z2);
[r,t]=cmath.polar(I1);
I2=I-I1;
[r1,t1]=cmath.polar(I2);
print"Current I1=",I1,"=",cmath.polar(I1),"=",round(r,3),"A"
print"Current I2=",I2,"=",cmath.polar(I2),"=",round(r1,3),"A"
#In the book the final answer is given in the polar form.

Current I1= (-5.40540540541+17.5675675676j) = (18.380365552345193, 1.869295258381076) = 18.38 A
Current I2= (5.40540540541+7.43243243243j) = (9.190182776172596, 0.9420000403794635) = 9.19 A


Ex2.63:pg-244¶

In [35]:
import cmath
V=120+1j*160;       #Assigning values to parameters
Z1=12+1j*16;
Z2=10-1j*20;
I1=V/Z1;
I2=V/Z2;
[r,t]=cmath.polar(Z1);
kW1=(V*I1*cos(t))/1000;
[r1,t1]=cmath.polar(kW1);
kVAR1=(V*I1*sin(t))/1000;
[r2,t2]=cmath.polar(kVAR1);
kVA1=(V*I1)/1000;
[r3,t3]=cmath.polar(kVA1);
[ro,th]=cmath.polar(Z2);
kW2=(V*I2*cos(th))/1000;
[r4,t4]=cmath.polar(kW2);
kVAR2=(V*I2*sin(th))/1000;
[r5,t5]=cmath.polar(kVAR2);
kVA2=(V*I2)/1000;
[r6,t6]=cmath.polar(kVA2);
Zeq=(Z1*Z2)/(Z1+Z2);
[R,T]=cmath.polar(Zeq);
pf=cos(T);
print"kW1=","=",kW1,cmath.polar(kW1),"=",round(r1,2)
print"kVAR1=",kVAR1,"=",cmath.polar(kVAR1),"=",round(r2,2)
print"kVA1=",kVA1,"=",cmath.polar(kVA1),"=",round(r3,2)
print"kW2=",kW2,"=",cmath.polar(kW2),"=",round(r4,2)
print"kVAR2=",kVAR2,"=",cmath.polar(kVAR2),"=",round(r5,2)
print"kVA2=",kVA2,"=",cmath.polar(kVA2),"=",round(r6,2)
print"Power factor=",round(pf,2)
#In the book the final answer is given in the polar form.

kW1= = (0.72+0.96j) (1.2000000000000002, 0.9272952180016122) = 1.2
kVAR1= (0.96+1.28j) = (1.5999999999999999, 0.9272952180016123) = 1.6
kVA1= (1.2+1.6j) = (2.0, 0.9272952180016123) = 2.0
kW2= (-0.78709592808+0.14310835056j) = (0.8000000000000002, 2.961739153797315) = 0.8
kVAR2= (1.57419185616-0.28621670112j) = (1.5999999999999999, -0.1798534997924783) = 1.6
kVA2= (-1.76+0.32j) = (1.7888543819998317, 2.961739153797315) = 1.79
Power factor= 1.0


Ex2.65:pg-246¶

In [52]:

R=30.0;              #Assigning values to parameters
I=5.0;
V=110.0;
f=50.0;
I1=V/R;
I2=sqrt(I**2-I1**2);
Xc=V/I2;
C=1.0/(2*math.pi*f*Xc);
print"Unknown capacitance when total current drawn is 5 A=",round(C,8),"Farad"
Inew=4.0;
I2new=sqrt(Inew**2-I1**2);
I2new1=round(I2new,2);
Xc=110/1.59;
f=1.0/(2*math.pi*C*Xc);
print"Frequency when total current drawn is 4 A=",round(f,2),"HZ"

Unknown capacitance when total current drawn is 5 A= 9.837e-05 Farad
Frequency when total current drawn is 4 A= 23.39 HZ


Ex2.66:pg-248¶

In [31]:
L1=0.0191             #Assigning values to parameters
f=50;
Xl1=2*math.pi*f*L1;
C=398*10**-6;
Xc=1/(2*math.pi*f*C);
L3=0.0318
Xl3=2*math.pi*f*L3;
Z1=2+1j*Xl1;
Z2=7-1j*Xc;
Z3=8+1j*Xl3;
Zeq=((Z1*Z2)/(Z1+Z2))+Z3;
[r,t]=cmath.polar(Zeq)
print"Equivalent Impedance=",Zeq,"=",cmath.polar(Zeq),"=",round(r,3),"ohms"
#In the book the final answer is given in the polar form.

Equivalent Impedance= (13.9532833128+14.2011622329j) = (19.908970942113147, 0.7942021909974325) = 19.909 ohms


Ex2.68:pg-251¶

In [30]:
Za=10+1j*8;                #Assigning values to parameters
Zb=9-1j*6;
Zc=3+1j*2;
V2=100;
I=V2/Zc;
Ia=(I*Zb)/(Za+Zb);
[r,t]=cmath.polar(Ia);
Ib=I-Ia;
[r1,t1]=cmath.polar(Ib);
print"Current Ia=",Ia,"=",cmath.polar(Ia),"=",round(r,4),"Amperes"
print"Current Ib=",Ib,"=",cmath.polar(Ib),"=",round(r1,3),"Amperes"

Current Ia= (4.48893572181-15.0474183351j) = (15.70271767770641, -1.2808821458253687) = 15.7027 Amperes
Current Ib= (18.5879873551-0.337197049526j) = (18.591045580170096, -0.018138600054248756) = 18.591 Amperes


Ex2.69:pg-252¶

In [28]:
import cmath
Im1=20.0;           #Assigning values to parameters
Im2=40.0;
Im=25.0;
#function i1=f(wt), i1=Im1*sin(wt), endfunction
#function i2=f(wt), i2=Im2*sin(wt+%pi/6), endfunction
#function i=f(wt), i=Im*sin(wt+%pi/6), endfunction
Z=6+1j*8;
I1=Im1/sqrt(2);
I2=24.49+1j*14.14;
I=15.31+1j*8.84;
I3=I-(I1+I2);
[r,t]=cmath.polar(I3);
V=I*Z;
[r1,t1]=cmath.polar(V);
P=V*I*cos(t);
[r2,t2]=cmath.polar(P);
Z1=V/I1;
[r3,t3]=cmath.polar(Z1);
print"Current I3=",I3,"=",cmath.polar(I3),"=",round(r,3),"Amperes"
print"Supply Voltage V=",V,"=",cmath.polar(V),"=",round(r1,3),"Volts"
print"Active Power P=",P,"=",cmath.polar(P),"=",round(r2,3),"Watts"
print"Impedance Z1=",Z1,"=",cmath.polar(Z1),"=",round(r3,3),"Ohms"

Current I3= (-23.3221356237-5.3j) = (23.916772567629184, -2.9181358418788084) = 23.917 Amperes
Supply Voltage V= (21.14+175.52j) = (176.78848944430746, 1.4509315848173419) = 176.788 Volts
Active Power P= (1197.41333962-2802.63102384j) = (3047.7105114663827, -1.167024701956722) = 3047.711 Watts
Impedance Z1= (1.49482373543+12.4111382234j) = (12.500833972179619, 1.4509315848173419) = 12.501 Ohms


Ex2.70:pg-255¶

In [11]:
Z=8.66+1j*5;      #Assigning values to parameters
Y=1.0/Z;
G=real(Y);
B=imag(Y);
print"G =",round(G,4),"Mho"
print"B =",round(-B,2),"Mho"

G = 0.0866 Mho
B = 0.05 Mho


Ex2.71:pg-255¶

In [26]:
import cmath
V=230.0;            #Assigning value to parameters
f=50.0;
Z1=8.66-5*1j;
Z2=10+17.32*1j;
Z3=40;
Y1=1.0/Z1;
[r1,t]=cmath.polar(Y1)
Y2=1.0/Z2;
[r2,t]=cmath.polar(Y2)
Y3=1.0/Z3;
[r3,t]=cmath.polar(Y3);
Y=Y1+Y2+Y3;
[r4,t]=cmath.polar(Y);
Z=1/Y;
[r,t]=cmath.polar(Z);
I=V/Z.real
[r5,t5]=cmath.polar(I);
pf=cos(t);
P=V*I*pf;
[r6,t6]=cmath.polar(P);
print"Y1=",Y1,"=",cmath.polar(Y1),"=",round(r1,2),"Mho"
print"Y2=",Y2,"=",cmath.polar(Y2),"=",round(r2,2),"Mho"
print"Y3=",Y3,"=",cmath.polar(Y3),"=",round(r3,3),"Mho"
print"Equivalent Impedance Z=",Z,"=",cmath.polar(Z),"=",round(r,3),"Ohms"
print"Total current I=",I,"=",cmath.polar(I),"=",round(r5,2),"Amperes"
print"Power consumed P=",P,"=",cmath.polar(P),"=",round(r6,2),"Watts"
print"Power factor pf=",round(pf,4)
#In the book the final answer is given in the polar form.

Y1= (0.0866038105677+0.0500022000968j) = (0.10000220007260266, 0.5236114777699694) = 0.1 Mho
Y2= (0.0250011000484-0.0433019052838j) = (0.05000110003630133, -1.0471848490249271) = 0.05 Mho
Y3= 0.025 = (0.025, 0.0) = 0.025 Mho
Equivalent Admittance Y= (0.136604910616+0.00670029481297j) = (0.13676913231794818, 0.049009434500553055) = 0.1368 Ohms
Equivalent Impedance Z= (7.30281212656-0.358193523139j) = (7.311591314883045, -0.049009434500553055) = 7.312 Ohms
Total current I= 31.4947168315 = (31.494716831541105, 0.0) = 31.49 Amperes
Power consumed P= 7235.08709962 = (7235.087099619459, 0.0) = 7235.09 Watts
Power factor pf= 0.9988


Ex2.72:pg-256¶

In [93]:
V=200;               #Assigning values to parameters
Z1=5*1j;
Z2=5+1j*8.66;
Z3=15;
Z4=-10*1j;
Y1=1.0/Z1;
Y2=1.0/Z2;
Y3=1.0/Z3;
Y4=1.0/Z4;
Yeq=Y1+Y2+Y3+Y4;
Zeq=1.0/Yeq;
I=V/Zeq;
[r,t]=cmath.polar(I);
print"Total current","=", I,"=",cmath.polar(I),"=",round(r,2),"A"
#In the book the final answer is given in the polar form.

Total current = (23.3337733527-37.3207621135j) = (44.01481868200551, -1.012037159177007) = 44.01 A


Ex2.73:pg-258¶

In [91]:
Xl=4.0;             #Assigning values to parameters
Xc=8.0;
Z1=1.0;
Z2=4*1j;
Z3=-1j*8;
Zeq=Z1+(Z2*Z3)/(Z2+Z3);
Y=1.0/Zeq;
[r,t]=cmath.polar(Y);
Xl=10.0;
Xc=5.0;
Z1=1.0;
Z2=10.0*1j;
Z3=-1j*5;
Zeq=Z1+(Z2*Z3)/(Z2+Z3);
Y=1.0/Zeq;
[r,t]=cmath.polar(Y);

Admittance= (0.0153846153846-0.123076923077j) = (0.12403473458920845, -1.446441332248135) = 0.124 Mho
Admittance= (0.00990099009901+0.0990099009901j) = (0.09950371902099893, 1.4711276743037347) = 0.0995 Mho


Ex2.74:pg-260¶

In [24]:
import cmath
Z1=14+1j*5;          #Assigning values to parameters
Z2=18+1j*10;
V=200;
Y1=1.0/Z1;
[r0,t0]=cmath.polar(Y1);
Y2=1.0/Z2;
[r3,t3]=cmath.polar(Y2);
Yeq=Y1+Y2;
[r4,t4]=cmath.polar(Yeq);
Zeq=1.0/Yeq;
I1=V/Z1;
[r5,t5]=cmath.polar(I1);
I2=V/Z2;
[r6,t6]=cmath.polar(I2);
I=V/Zeq;
[r7,t7]=cmath.polar(I);
P1=I1**2*real(Z1);
[r8,t8]=cmath.polar(P1);
P2=I2**2*real(Z2);
[r9,t9]=cmath.polar(P2);
[r,t]=cmath.polar(Zeq);
[r1,t1]=cmath.polar(Z1);
[r2,t2]=cmath.polar(Z2);
pf1=cos(t1);
pf2=cos(t2);
pf=cos(t);
print"Y1=",Y1,"=",cmath.polar(Y1),"=",round(r0,3),"Mho"
print"Y2=",Y2,"=",cmath.polar(Y2),"=",round(r3,3),"Mho"
print"Yeq=",Yeq,"=",cmath.polar(Yeq),"=",round(r4,3),"Mho"
print"Branch current I1=",I1,"=",cmath.polar(I1),"=",round(r5,3),"Amperes"
print"Branch current I2=",I2,"=",cmath.polar(I2),"=",round(r6,3),"Amperes"
print"Total current I=",I,"=",cmath.polar(I),"=",round(r7,2),"Amperes"
print"Power consumed by branch1=",P1,"=",cmath.polar(P1),"=",round(r8,3),"Watts"
print"Power consumed by branch2=",P2,"=",cmath.polar(P2),"=",round(r9,3),"Watts"
print"Power factor of branch1=",round(pf1,3)
print"Power factor of branch2=",round(pf2,3)
print"Total Power factor=",round(pf,3)

Y1= (0.0633484162896-0.0226244343891j) = (0.06726727939963124, -0.3430239404207034) = 0.067 Mho
Y2= (0.0424528301887-0.0235849056604j) = (0.04856429311786321, -0.507098504392337) = 0.049 Mho
Yeq= (0.105801246478-0.0462093400495j) = (0.11545218431960486, -0.41178588495508256) = 0.115 Mho
Branch current I1= (12.6696832579-4.52488687783j) = (13.45345587992625, -0.3430239404207034) = 13.453 Amperes
Branch current I2= (8.49056603774-4.71698113208j) = (9.712858623572641, -0.507098504392337) = 9.713 Amperes
Total current I= (21.1602492957-9.2418680099j) = (23.09043686392097, -0.41178588495508256) = 23.09 Amperes
Power consumed by branch1= (1960.64781638-1605.20873856j) = (2533.9366515837105, -0.6860478808414068) = 2533.937 Watts
Power consumed by branch2= (897.116411534-1441.79423282j) = (1698.1132075471692, -1.014197008784674) = 1698.113 Watts
Power factor of branch1= 0.942
Power factor of branch2= 0.874
Total Power factor= 0.916


Ex2.75:pg-262¶

In [22]:
import cmath
V=230;         #Assigning values to parameters
f=50;
L=0.08;
Xl=2*math.pi*f*L;
C=200*10**-6;
Xc=1/(2*math.pi*f*C);
Z1=20+1j*25.13;
Z2=10-1j*15.92;
Y1=1.0/Z1;
Y2=1.0/Z2;
Y=Y1+Y2;
I=V*Y;
[r,t]=cmath.polar(I);
pf=cos(t);
Z=1.0/Y;
[r1,t1]=cmath.polar(Z)
R=real(Z);
Xc=-1*imag(Z);
C=1.0/(2*math.pi*f*Xc);
[r2,t2]=cmath.polar(C);
print"Supply Current=",I,"=",cmath.polar(I),"=",round(r,2),"A"
print"Power factor=",round(pf,3)
print"Total impedance=",Z,"=",cmath.polar(Z),"=",round(r1,2),"Ohms"
print"Resistance of eequivalent series circuit=",R,"=",cmath.polar(R),"=",round(r1,2),"Ohms"
print"Capacitance of eequivalent series circuit=",C,"=",cmath.polar(C),"=",round(r2,5),"Farads"

Supply Current= (10.9668035101+4.75640244987j) = (11.953833840878367, 0.40922414432872894) = 11.95 A
Power factor= 0.917
Total impedance= (17.6519817092-7.6558250514j) = (19.240689059393823, -0.409224144328729) = 19.24 Ohms
Resistance of eequivalent series circuit= 17.6519817092 = (17.651981709220966, 0.0) = 19.24 Ohms
Capacitance of eequivalent series circuit= 0.000415774765028 = (0.0004157747650276909, 0.0) = 0.00042 Farads


Ex2.76:pg-263¶

In [77]:
V=200;          #Assigning values to parameters
Z1=3+4*1j;
Z2=4-1j*3;
Z3=4.57+1j*5.51;
Y1=1.0/Z1;
Y2=1.0/Z2;
Yab=Y1+Y2;
Zab=1.0/Yab;
Z=Zab+Z3;
[r,t]=cmath.polar(Z);
I=V/r
pf=cos(t);
print"Total Impedance=",Z,"=",cmath.polar(Z),"=",round(r,2),"Ohms"
print"Supply current=",round(I,2),"A"
print"Power factor=",round(pf,4)

Total Impedance= (8.07+6.01j) = (10.06205744368417, 0.6401220717631577) = 10.06 Ohms
Supply current= 19.88 A
Power factor= 0.802


Ex2.77:pg-268¶

In [20]:
C=2.5*10**-6;         #Assigning values to parameters
R=15.0;
L=260*10**-3;
temp=(1.0/(L*C))-(R**2/L**2);
fr=(1.0/20*math.pi)*sqrt(temp);
Q=(2*math.pi*fr*L)/R;
Zr=L/(C*R);
print"Resonant frequeny=",round(fr,2),"Hertz"
print"Quality factor=",round(Q,2)
print"Dynamic Impedance=",round(Zr,2),"Ohms"
#the answer of the fr in the book is wrong

Resonant frequeny= 194.62 Hertz
Quality factor= 21.2
Dynamic Impedance= 6933.33 Ohms


Ex2.78:pg-268¶

In [87]:
import math
C=200*10**-6;         #Assigning values to parameters
V=230.0;
R=20.0;
L=0.2;
temp=((1.0/(L*C))-(R**2/L**2));
fr=sqrt(temp)/(2*math.pi);
Zr=L/(C*R);
Ir=V/Zr;
Zl=sqrt(R**2+(2*math.pi*fr*L)**2);
Il=V/Zl;
Xc=1.0/(2*math.pi*fr*C);
Ic=V/Xc;
phi=math.atan(2*math.pi*fr*L/R);
phi=math.degrees(phi);
print"Resonant frequency",round(fr,2),"Hertz"
print"Dynamic impedance of the circuit=",round(Zr,2),"Ohms"
print"circuit current Ir=",round(Ir,2),"A"
print"current Il=",round(Il,2),"A"
print"current Ic=",round(Ic,2),"A"
print"phase angle of the coil phi=",round(phi,2),"degrees"

Resonant frequency 19.49 Hertz
Dynamic impedance of the circuit= 50.0 Ohms
circuit current Ir= 4.6 A
current Il= 7.27 A
current Ic= 5.63 A
phase angle of the coil phi= 50.77 degrees


Ex2.79:pg-270¶

In [39]:
pfcoil=0.3;           #Assigning values to parameters
phi=math.acos(pfcoil);
V=100.0;
f=50.0;
Il=1.0;
Ic=Il*sin(phi);
Xc=V/Ic;
C=1.0/(2*math.pi*f*Xc);
Ir=Il*cos(phi);
Zr=V/Ir;
print"Dynamic impedance=",round(Zr,2),"Ohms"

Capacitance= 3.036e-05 Farads
Dynamic impedance= 333.33 Ohms


Ex2.80:pg-271¶

In [83]:
V=200.0;       #Assigning values to parameters
f=50.0;
L=20.0;
R=15.0;
Zl=sqrt(R**2+L**2);
pfcoil=R/Zl;
phi=math.acos(pfcoil);
Il=V/Zl;
Ic=Il*sin(phi);
Xc=V/Ic;
C=1/(2*math.pi*f*Xc);
Ir=Il*math.cos(phi);
print"Power factor=",round(pfcoil,2)
print"Current=",round(Il.real,2),"A"
print"Value f shunting capacitance=","{:.4e}".format(C),"Farads"
print"Circuit current at resonance=",round(Ir.real,2),"A"

Power factor= 0.6
Current= 8.0 A
Value f shunting capacitance= 1.0186e-04 Farads
Circuit current at resonance= 4.8 A