Chapter 3 : Single Phase AC Circuits

Example 3.1 Page No : 3.7

In [1]:
import math 

# Variables
N = 100.;				#turns
R = 1500.;				#rpm(Rotation)
B = 0.05;				#T(Magnetic field)
A = 40.;				#cm**2(Cross sectional area)

# Calculations and Results
f = R/60;				#Hz
theta = 30.;				#degree
print "(a) Frequency(Hz) : %.2f"%f

Period = 1/f;				#seconds
print "(b) Period(seconds) : %.2f"%Period

Em = 2*math.pi*B*(A/10**4)*N*f;				#V
print "(c) Maximum value of gnerated emf(V) : %.2f"%Em

e = math.pi*math.sin(math.radians(theta));				#V
print "(d) Gnerated emf after rotation(V) : %.2f"%e

(a) Frequency(Hz) : 25.00
(b) Period(seconds) : 0.04
(c) Maximum value of gnerated emf(V) : 3.14
(d) Gnerated emf after rotation(V) : 1.57

Example 3.2 Page No : 3.12

In [3]:
import math 

# Variables
Irms = 10;				#A

# Calculations
Im = Irms*math.sqrt(2);				#A

# Results
print "Peak values of current(A) are :%.2f and %.2f"%(+Im,-Im)

Peak values of current(A) are :14.14 and -14.14

Example 3.3 Page No : 3.12

In [5]:
import math 

# Variables
#v = 141.4*math.sin(377*t)
Vm = 141.4;				#V

# Calculations and Results
V = Vm/math.sqrt(2);				#V(rms voltage)
print "(a) r.m.s. Voltage(V) : %.f"%V

omega = 377.;				#rad/s
f = omega/2/math.pi;				#Hz
print "(b) Frequency(Hz) : %.2f"%f

t = 3*10**-3;				#seconds
v = 141.4*math.sin(377*t);				#V
print "(c) Instantaneous Voltage(V) : %.2f"%v

(a) r.m.s. Voltage(V) : 100
(b) Frequency(Hz) : 60.00
(c) Instantaneous Voltage(V) : 127.94

Example 3.4 Page No : 3.13

In [6]:
import math 

# Variables
V = 110.;				#V(Supply voltage)
R = 50.;				#ohm

# Calculations and Results
Vm = V*math.sqrt(2);				#V(maximum voltage)
Im = Vm/R;				#A(maximum current)
Iav1 = 0.637*Im;				#A(average current Over +ve half cycle)
Iav2 = 0;				#(average current Over -ve half cycle)
Iav = (Iav1+Iav2)/2;				#A(average current Over whole cycle)
print "(a) Reading on moving coil ammeter(A) : %.2f"%Iav

#For thermal ammeter : I**2*R = 1/4*Im**2*R(thermal effect for complete cycle)
I = math.sqrt(1./4*Im**2);				#A(reading on thermal ammeter)
print "(a) Reading on thermal ammeter(A) : %.2f"%I

kf = I/Iav;				#form factor
kp = Im/I;				#peak factor
print "(b) Form factor & peak factor are : %.2f and %.2f"%(kf,kp)

(a) Reading on moving coil ammeter(A) : 0.99
(a) Reading on thermal ammeter(A) : 1.56
(b) Form factor & peak factor are : 1.57 and 2.00

Example 3.5 Page No : 3.21

In [10]:
import math 

V = 100.;				#V
R = 7.;				#ohm
L = 31.8;				#mH
f = 50.;				#/Hz
XL = 2*math.pi*f*L/1000;				#ohm
Z = math.sqrt(R**2+XL**2);				#ohm
I = V/Z;				#A(circuit current)
print "(a) Circuit current(A) %.1f"%I

fi = math.degrees(math.atan(XL/R));				#degree(lag)
print "(b) Phase angle(lag) in degree : %.f"%fi 

(a) Circuit current(A) 8.2
(b) Phase angle(lag) in degree : 55

Example 3.6 Page No : 3.21

In [12]:
import math 

# Variables
L = 318.;				#mH
R = 75.;				#ohm
VR = 150.;				#V
f = 50.;				#/Hz

# Calculations
I = VR/R;				#A
XL = 2*math.pi*f*L/1000;				#ohm
VL = I*XL;				#V
V = math.sqrt(VR**2+VL**2);				#V

# Results
print "Supply Voltage(V) : %.f"%V

Supply Voltage(V) : 250

Example 3.7 Page No : 3.21

In [22]:
import math 

# Variables
ZLr = 50.;				#ohm
fiLr = 45.;				#degree(lag)(between current & Voltage)
R = 40.;				#ohm
I = 3.;				#A(Circuit current)

# Calculations and Results
VR = I*R;				#V
VLr = I*ZLr;				#V
V = math.sqrt(VR**2+VLr**2+2*VR*VLr*math.cos(math.radians(fiLr)));				#V
print "Supply voltage(V) : %.f"%V
print math.cos(math.radians(fiLr))
fi = math.degrees(math.acos((VR+VLr*math.cos(math.radians(fiLr)))/V));				#degree
print "Circuit phase angle(lag in degree) : %.f"%fi

Supply voltage(V) : 250
0.707106781187
Circuit phase angle(lag in degree) : 25

Example 3.8 Page No : 3.24

In [23]:
import math 

# Variables
C = 30.;				#micro F
V = 400.;				#V
f = 50.;				#Hz

# Calculations and Results
Xc = 1/(2*math.pi*f*C*10**-6);				#ohm
print "(a) Reacmath.tance of capacitor(ohm) : %.2f"%Xc

I = V/Xc;				#A
print "(b) Current(A) : %.2f"%I

(a) Reacmath.tance of capacitor(ohm) : 106.10
(b) Current(A) : 3.77

Example 3.9 Page No : 3.26

In [25]:
import math 

# Variables
R = 12.;				#ohm(Coil Resistance)
L = 0.1;				#H(Coil Inductance)
V = 100.;				#V
f =  50.;				#Hz

# Calculations and Results
XL = 2*math.pi*f*L;				#ohm
Z = math.sqrt(R**2+XL**2);				#ohm
print "(a) Reactance(ohm) & impedence(ohm) of the coil are : %.2f and %.2f"%(XL,Z)

I = V/Z;				#A
print "(b) Current(A) : %.2f"%I

fi = math.degrees(math.atan(XL/R));				#degree
print "Phase difference(degree) : %.f"%fi

(a) Reactance(ohm) & impedence(ohm) of the coil are : 31.42 and 33.63
(b) Current(A) : 2.97
Phase difference(degree) : 69

Example 3.10 Page No : 3.27

In [26]:
import math 

# Variables
Pr = 750.;				#W(rated)
Vr = 100.;				#V(rated)
V = 230.;				#V(Supply voltage)
f = 60.;				#Hz

# Calculations and Results
VC = math.sqrt(V**2-Vr**2);				#V(Voltage across capacitor)
Ir = Pr/Vr;				#A(Rated current)
C = Ir/(2*math.pi*f*VC)*10**6;				#micro F
print "(a) Capacimath.tance required(micro F) : %.2f"%C

fi = math.acos(math.radians(Vr/V));				#degree
print "(b) Phase angle(degree) : %.2f"%fi

(a) Capacimath.tance required(micro F) : 96.05
(b) Phase angle(degree) : 1.56

Example 3.11 Page No : 3.27

In [28]:
import math 

# Variables
R = 12.;				#ohm
L = 0.15;				#H
C = 100.;				#micro F
V = 100.;				#V
f = 50.;				#Hz

# Calculations and Results
XL = 2*math.pi*f*L;				#ohm
XC = 1/(2*math.pi*f*C*10**-6);				#ohm
Z = math.sqrt(R**2+(XL-XC)**2);				#ohm
print "(a) Impedence(ohm) : %.2f"%Z

I = V/Z;				#A
print "(b) Current(A) : %.2f"%I

VR = R*I;				#V
VL = XL*I;				#V
VC = XC*I;				#V
print "(b) Voltge(V) across R, L & C : %.2f , %.2f and %.2f"%(VR,VL,VC)

fi = math.degrees(math.acos(VR/V));				#degree
print "(c) Phase difference(degree): %.2f"%fi

(a) Impedence(ohm) : 19.44
(b) Current(A) : 5.14
(b) Voltge(V) across R, L & C : 61.73 , 242.42 and 163.75
(c) Phase difference(degree): 51.88

Example 3.12 Page No : 3.33

In [29]:
import math 

# Variables
R = 6.;				#ohm
L = 0.03;				#H
V = 50.;				#V
f = 60.;				#Hz

# Calculations and Results
XL = 2*math.pi*f*L;				#ohm
Z = math.sqrt(R**2+XL**2);				#ohm
I = V/Z;				#A
print "(a) Current(A) : %.2f"%I

fi = math.degrees(math.atan(XL/R));				#degree
print "(b) Phase angle(degree) : %.2f"%fi

S = V*I;				#VA(Apparent power)
print "(c) Apparent power(VA) : %.2f"%S

P = S*math.cos(math.radians(fi));				#W
print "(d) Active power(W) : %.f"%P

(a) Current(A) : 3.91
(b) Phase angle(degree) : 62.05
(c) Apparent power(VA) : 195.27
(d) Active power(W) : 92

Example 3.13 Page No : 3.34

In [31]:
import math 

# Variables
R = 30.;				#ohm
V = 230.;				#V
f = 50.;				#Hz
VR = 130.;				#V
VLr = 180.;				#V

# Calculations
fiLr = math.degrees(math.acos((V**2-VR**2-VLr**2)/(2*VR*VLr)));				#degree(lag)
I = VR/R;				#A
Pr = VLr*I*math.cos(math.radians(fiLr));				#W

# Results
print "Power dissipated in the coil(W) : %.2f"%Pr

Power dissipated in the coil(W) : 60.00

Example 3.14 Page No : 3.35

In [32]:
import math 

# Variables
V = 230.;				#V
f = 50.;				#Hz
I = 5.;				#A
P = 750.;				#W

# Calculations and Results
Z = V/I;				#ohm
R = P/I**2;				#ohm(Resistance)
XL = math.sqrt(Z**2-R**2);				#ohm(reacmath.tance)
L = XL/2/math.pi/f;				#H(Inductance)
print "(a) Resistance(ohm) : %.2f"%R
print "(a) Inductance(mH) : %.2f"%(L*1000)

pf = P/(V*I);				#power factor(lag)
print "(b) Power factor(lag) : %.2f "%pf

(a) Resistance(ohm) : 30.00
(a) Inductance(mH) : 111.00
(b) Power factor(lag) : 0.65