# Chapter 11: Single Phase A-C Circuits¶

### Example 11.1: page 211:¶

In :
from __future__ import division
import math

#given  data  :
E_max=500;#  emf  in  volts
thita=30;#  in  degree

#calculations:
e=E_max*math.sin(thita*math.pi/180);

#Results
print  "instantaneous  value,e(v)  =  ",e

instantaneous  value,e(v)  =   250.0


### Example 11.2: page 212:¶

In :
from __future__ import division
import math

#given  data  :
I_max=1.414;#  maximum  value  of  current  in  A

#calculations:
I_rms=I_max*0.707;

#Results
print  "rms  value  of  current,I_rms(A) = ",round(I_rms)

rms  value  of  current,I_rms(A) =  1.0


### Example 11.3: page 220:¶

In :
from __future__ import division
import math

#given  data  :
f=50;#  frequency  in  Hz
L=0.2;#  inductance  in  H
V=220;#  voltage  in  volts

#calculations:
XL=2*math.pi*f*L#  in  ohm
Z=XL;
I=V/Z;

#Results
print  "current  drawn,I(A)  =  ",round(I,2)

current  drawn,I(A)  =   3.5


### Example 11.4: page 222:¶

In :
from __future__ import division
import math

#given  data  :
f=50;#  frequency  in  Hz
C=100*10**-6#  capacitor  in  Farad
V=210;#  voltage  in  volts

#calculations:
XC=(1/(2*math.pi*f*C));
Z=XC;
I=V/Z;

#Results
print  "current  flowing,I(A)  =  ",round(I,2)

current  flowing,I(A)  =   6.6


### Example 11.5: page 222:¶

In :
from __future__ import division
import math

#given  data  :
f=50;#  frequency  in  Hz
L=0.4;#  inductance  in  H
V=220;#  voltage  in  volts
f1=25;#  frequency  is  halved
f2=100;#  frequency  is  doubled

#calculations:
XL=2*math.pi*f*L;
I=V/XL;

XL1=2*math.pi*f1*L;
I1=V/XL1;

XL2=2*math.pi*f2*L;
I2=V/XL2;

#Results
print  "current  flowing,I(A)  =  ",round(I,2)
print  "(a)current  when  frequency  is  halved,I(A)  =  ",round(I1,2)
print  "current  when  frequency  is  doubled,I(A)  =  ",round(I2,3)

current  flowing,I(A)  =   1.75
(a)current  when  frequency  is  halved,I(A)  =   3.5
current  when  frequency  is  doubled,I(A)  =   0.875


### Example 11.6: page 223:¶

In :
from __future__ import division
import math

#given  data  :
f=50;#  frequency  in  Hz
C=28*10**-6#  capacitor  in  Farad
V=250;#  voltage  in  volts
f1=25#  when  frequency  is  halved
f2=100#  when  frequency  is  doubled

#calculations:
XC=1/(2*math.pi*f*C);
I=V/XC;

XC1=1/(2*math.pi*f1*C);
I1=V/XC1;

XC2=1/(2*math.pi*f2*C);
I2=V/XC2;

#Results
print  "current  flowing,I(A)  =  ",round(I,1)
print  "current  flowing  when  frequency  is  halved,I(A)  =  ",round(I1,1)
print  "current  flowing  when  frequency  is  doubled  ,I(A)  =",round(I2,1)

current  flowing,I(A)  =   2.2
current  flowing  when  frequency  is  halved,I(A)  =   1.1
current  flowing  when  frequency  is  doubled  ,I(A)  = 4.4


### Example 11.7: Page 224:¶

In :
from __future__ import division
import math

#given data:
R=40  #in  ohms
L=0.07#IN  HENRY
V=223#IN  VOLTS
F=50  #  IN  HERTS

#calculations:
Xl=2*math.pi*F*L#  inductive  reactance  in  ohms
Z=(R**2+Xl**2)**0.5#IMPEDENCE  IN  OHMS
I=V/Z;#in  amperes
csp=R/Z#pf
phi=math.acos(csp)#angle  of  phase  differnce  in  degree

def decdeg2dms(dd):
mnt,sec = divmod(dd*3600,60)
deg,mnt = divmod(mnt,60)
return deg,mnt,sec
phiAct = decdeg2dms(phi*180/math.pi)

#Results
print  "inductive  reactance  in  ohms  is",round(Xl)
print  "impedence  in  ohms  is",round(Z,2)
print  "current  in  amperes  is",round(I,1)
print  "angle  of  phase  difference  is  ",phiAct,"Degrees and ",phiAct,"minutes"

inductive  reactance  in  ohms  is 22.0
impedence  in  ohms  is 45.65
current  in  amperes  is 4.9
angle  of  phase  difference  is   28.0 Degrees and  48.0 minutes


### Example 11.8: Page 226:¶

In :
from __future__ import division
import math

#given data:
V=200#in  volts
I=2.5#  in  amperes
Vo=250#  in  volts
f=50  #  in  hertz

#calculations:
R=V/I#  in  ohms
Z=Vo/I#  in  ohms
Xl=(Z**2-R**2)**0.5#inductive  reactance  in  ohms
L=(Xl/(2*math.pi*f))#inductance  in  henry
pf=R/Z#power  factor
phi=math.acos(pf)#angle  of  phase  differnce  in  degree
def decdeg2dms(dd):
mnt,sec = divmod(dd*3600,60)
deg,mnt = divmod(mnt,60)
return deg,mnt,sec
phiAct = decdeg2dms(phi*180/math.pi)

#Results
print  "inductance  in  henry  is",round(L,4)
print  "angle  of  phase  difference  is  ",phiAct,"Degrees and ",phiAct,"minutes"

inductance  in  henry  is 0.191
angle  of  phase  difference  is   36.0 Degrees and  52.0 minutes


### Example 11.9: page 226:¶

In :
from __future__ import division
import math

#given data:
W=100#in  watts
V=110#in  volts
Vc=220#in  volts
f=50  #in  hertz

#calculations:
I=W/V#  in  amperes
R=V/I#in  ohms
Z=Vc/I#  in  ohms
Xc=math.sqrt(Z**2-R**2)#  IN  OHMS
C=(1/(2*math.pi*f*Xc))#  in  farads

#Results
print  "capacitance  in  micro  farads  is",round(C*10**6,2)

capacitance  in  micro  farads  is 15.19


### Example 11.10: page 227:¶

In :
from __future__ import division
import math

#given data:
R=5.94#in  ohms
L=0.35#IN  HENRY
C=35  #  in  micro  farads
V=220#IN  VOLTS
F=50  #  IN  HERTS

#calculations:
Xc=(1/(2*math.pi*F*C*10**-6))#  capacitive  reactance  in  ohms
Xl=2*math.pi*F*L#  inductive  reactance  in  ohms
Z=math.sqrt(R**2+(Xl-Xc)**2)#  impedence  in  ohms
I=V/round(Z)#  in  amperes
pf=R/round(Z)#  power  factor
Zc=math.sqrt(R**2+Xl**2)#impedence  of  the  coil
Vl=I*Zc#voltage  drop  across  the  coil
Vc=I*Xc#voltage  drop  across  the  capacitor
W=I**2*R#total  power  taken  in  watts

#Results
print  "(a)impedence  in  ohms  is",round(Z)
print  "(b)current  in  amperes  is",I
print  "(c)angle  of  phase  diffence  between  voltage  and  current  is",pf
print  "(d)voltage  across  the  coil  in  volts  is",round(Vl,1)
print  "(e)voltage  across  capacitor  in  volts  is",round(Vc,1)
print  "(f)total  power  taken  in  watts  is",round(W,1)

(a)impedence  in  ohms  is 20.0
(b)current  in  amperes  is 11.0
(c)angle  of  phase  diffence  between  voltage  and  current  is 0.297
(d)voltage  across  the  coil  in  volts  is 1211.3
(e)voltage  across  capacitor  in  volts  is 1000.4
(f)total  power  taken  in  watts  is 718.7


### Example 11.11: page 233:¶

In :
from __future__ import division
import math

#given data:
r1=6  #in  ohms
r2=3.95#in  ohms
R=r1+r2#in  ohms
L1=0.21#IN  HENRY
L2=0.14#in  henry
C1=30#  in  micro  farads
C2=60#in  micro  farads
V=220#IN  VOLTS
F=50  #  IN  HERTS

#calculations:
Xc1=(1/(2*math.pi*F*C1*10**-6))#  capacitive  reactance  in  ohms
Xc2=(1/(2*math.pi*F*C2*10**-6))#  capacitive  reactance  in  ohms
Xc=Xc1+Xc2#IN  OHMS
Xl1=2*math.pi*F*L1#  inductive  reactance  in  ohms
Xl2=2*math.pi*F*L2#  inductive  reactance  in  ohms
Xl=Xl1+Xl2#in  ohms
Z=math.sqrt(R**2+(Xl-Xc)**2)#  impedence  in  ohms
I=V/Z#
pf=R/Z#  leading  power  factor

#Results
print  "(a)impedence  in  ohms  is",round(Z)
print  "(b)current  in  amperes  is",round(I)
print  "(c)power  factor  (leading)  is",round(pf,3)

(a)impedence  in  ohms  is 50.0
(b)current  in  amperes  is 4.0
(c)power  factor  (leading)  is 0.198


### Example 11.12: Page 233:¶

In :
from __future__ import division
import math

#given data:
V=200#  in  volts
L=0.04#  in  henry
C=100#in  micro  fards
f=50  #  hertz
Z1=10#ohms
R1=10#  in  ohms
X1=0  #  in  ohms
R2=5  #  in  ohms
R3=15#  in  ohms

#calculations:
Xl=2*math.pi*f*L#inductive  reactance  in  ohms
Xc=(1/(2*math.pi*f*C*10**-6))#CAPACITIVE  REACTANCE  IN  OHMS
Z2=math.sqrt(R2**2+Xl**2)#in  ohms
X2=Xl#
Z3=math.sqrt(R3**2+Xc**2)#  IN  OHMS
X3=Xc#
g1=R1/(Z1)**2#  conductance  of    branch  1  in  mho
b1=X1/(Z1)**2#susceptance  in  mho  in  branch  1
g2=R2/(Z2)**2#  conductance  of    branch  2  in  mho
b2=X2/(Z2)**2#susceptance  in  mho  in  branch  2
g3=R3/(Z3)**2#  conductance  of    branch  3  in  mho
b3=X3/(Z3)**2#susceptance  in  mho  in  branch  3
G=g1+g2+g3#  total  conductance  in  mho
B=b1+b2-b3#  total  susceptance  in  mho
Y=math.sqrt(G**2+B**2)#in  ohms
I0=V*Y#curent  in  ampere
theta=math.acos(G/Y)#

def decdeg2dms(dd):
mnt,sec = divmod(dd*3600,60)
deg,mnt = divmod(mnt,60)
return deg,mnt,sec
phiAct = decdeg2dms(theta*180/math.pi)

I=V/Z3#curent  in  amperes
pf3=R3/Z3#power  factor
phi=math.acos(pf3)#angle  of  phase  differnce  in  degree

tc3=pf3#
ts3=math.sin(phi)
pf1=R1/R1#
tc1=pf1#
ts1=math.sin(math.acos(pf1))#
I1=V/Z1#
E1=I1*tc1#  energy  component  in  branch  1
EL1=I1*ts1#  idel  current  component  in  branch  1
I2=V/Z2#
pf2=R2/Z2#
tc2=pf2#
ts2=math.sin(math.acos(pf2))#
E2=I2*tc2#ENERGY  COMPONENT  IN  BRANCH2
EL2=I2*ts2#idele  current  component  in  branch  2
E3=I*tc3#energy  component  in  branch3
EL3=I*ts3#idle  component  of  current  in  branch  3
E=E1+E2+E3#sum  of  energy  component  of  current
EL=EL1+EL2-EL3#sum  of  idel  component  of  current
It=math.sqrt(E**2+EL**2)#  total  current
pft=E/It#power  factor  of  the  complete  circuit
phi=math.acos(0.95)#angle  of  phase  differnce  in  degree

Zt=V/It#in  ohms
R=Zt*pft#equivalent  series  resistance
X=Zt*(math.sin(phi))#equivalent  series  reactance

#Results
print "(a)current  in  amperes  is",round(I0)
print  "Phase angle  is  ",phiAct,"Degrees and ",phiAct,"minutes"
print  "(c)equivalent  series  resistance  in  ohms  is",round(R,2)
print  "euivalent  series  reactance  in  ohms  is",round(X,3)

(a)current  in  amperes  is 29.0
Phase angle  is   17.0 Degrees and  8.0 minutes
(c)equivalent  series  resistance  in  ohms  is 6.55
euivalent  series  reactance  in  ohms  is 2.14