Chapter 3: Electricity and its Fundamental Laws

Example 3.1: Page 47

In [2]:
from __future__ import division
import math

#given data:
V = 230;    #  in  volts
I = 10;     #  in  A

# calculations:
R = V/I;

#Results
print "resistance  of  element,R =", R,"ohm" 

resistance  of  element,R = 23.0 ohm

Example 3.2: Page 47

In [1]:
from __future__ import division
import math

#given  data  :
R1 = 0.5;   #  minimum  value  of  resistance  in  ohm
R2 = 20;    #  maximum  value  of  resistance  in  ohm
I  = 1.2;   #  current  in  A

#Calculation
V1 = I*R1;
V2 = I*R2;

#Results
print  "Voltage  drop  in  Ist  case,V1(V)=",V1,"volts and voltage  drop  in  IInd  case,V2(V)=", V2,"volts"

Voltage  drop  in  Ist  case,V1(V)= 0.6 volts and voltage  drop  in  IInd  case,V2(V)= 24.0 volts

Example 3.3: Page 48

In [3]:
from __future__ import division
import math

#given  data  :
L  = 1000;  #  length  of  wire  in  cm
d  = 0.14;  #  diameter  of  wire  in  cm
R1 = 2.5*10**6;#  resistance  in  micro-ohm

# calculations:
a  = (math.pi*d**2)/4;  #  cross  section  area
p  = (R1*a)/L;

#Results
print  "the  specific  resistance,p =", round(p,1)," uOhm-cm" 

the  specific  resistance,p = 38.5  uOhm-cm

Example 3.4: Page 49

In [4]:
from __future__ import division
import math

#given  data  :
Rt1  = 54.3;#    resistance  in  ohm
alfa = 0.0043;#  the  resistance  temperature  of  coeficient  in  per  degree  celcius
t1   = 20;#  temperature  in  degree  celcius
t2   = 40;#  temperature  in  degree  celcius

# calculations
Rt2  = (Rt1*(1+(alfa*t2)))/(1+(alfa*t1));

#Results
print  "resistance  at  40 degC ,Rt2=", Rt2," ohms" 

resistance  at  40 degC ,Rt2= 58.6  ohms

Example 3.5: Page 50

In [4]:
from __future__ import division
import math

#given  data  :
r1=30;#    resistance  in  ohm
r2=35;#    resistance  in  ohm
r3=45;#    resistance  in  ohm
V=220;

# calculations:
R=r1+r2+r3;
I=V/R;

#Results
print  "(a)total  resistance,R=", R," ohm"
print  "(b)current,I=", I,"A" 

(a)total  resistance,R= 110  ohm
(b)current,I= 2.0 A

Example 3.6: Page 50

In [6]:
from __future__ import division
import math

#given  data  :
I=75;#  current  in  A
R=0.15;#  resistance  in  ohm
v=220;#  voltage  in  volts

#calculations
V1=I*R;#  voltage  drop  of  the  feeder  in  section  AB
V2=I*R;#  voltage  drop  of  the  feeder  in  section  CD
V_total=V1+V2;#  total  voltage  drop  in  the  lead  and  return  feeder
V=v+V_total;

#Results
print  "voltage  at  the  generating  station,V=", V,"volts" 

voltage  at  the  generating  station,V= 242.5 volts

Example 3.7: Page 52

In [7]:
from __future__ import division
import math

#given  data  :
r1=6;#    resistance  in  ohm
r2=10;#    resistance  in  ohm
r3=15;#    resistance  in  ohm

#calculations:
r=(1/r1)+(1/r2)+(1/r3);
R=1/r;

#Results
print  "equivalent  resistance,R=", R,"ohm" 

equivalent  resistance,R= 3.0 ohm

Example 3.8: Page 53

In [8]:
from __future__ import division
import math

#given  data  :
I=5;  #  current  in  A
n=2;  #  number  of  resistance  in  parallel  of  section  BC
r1=15;#    resistance  in  ohm
r2=20;#    resistance  in  ohm
r3=60;#    resistance  in  ohm
r4=64;#    resistance  in  ohm
r5=64;#    resistance  in  ohm
r6=2.5;#    resistance  in  ohm

#calculation
R1=r4/n;#  equivalent  resistance  of  section  BC
R2=(r1*r2*r3)/((r1*r2)+(r2*r3)+(r3*r1));#  equivalent  resistance  of  section  CD
R=R1+R2+r6;#  equivalent  resistance  of  section  AD
V=I*R;

#Results
print  "voltage,V= ", V,"volts" 

voltage,V=  210.0 volts

Example 3.9: Page 53

In [9]:
from __future__ import division
import math

#given  data  :
V=240;#  voltage  in  volts
r1=2;#  resistance  in  ohm
r2=3;#  resistance  in  ohm
r3=8.8;#  resistance  in  ohm
r4=10;#  resistance  in  ohm
r5=3;#  resistance  in  ohm

# calculations:
R1=(r1*r2)/(r1+r2);#  equivalent  resistance  of  parallel  branch
R2=R1+r3;#  equivalent  resistance  of  section  ABC
R3=(R2*r4)/(R2+r4);
R=R3+r5;#  total  resistance  of  section  AD
I=V/R;
V1=I*r5;#  voltage  drop  across  r5
V2=V-V1;#  voltage  drop  across  section  ABC
I1=V2/r4;#  current  flowing  through  r4  resistance
I2=I-I1;#  current  in  r3  resistance
V3=I2*r3;#  voltage  drop  across  r3  resistance,  section  ABC
V4=V2-V3;#  voltage  drop  between  section  AB
I3=V4/r1;#  current  flowing  through  r1  resistance
I4=V4/r2;#    current  flowing  through  r2  resistance

#Results
print  "current  flowing  through  r1  (2  ohms)  resistance,I3  =", I3," A"
print  "current  flowing  through  r2  (3  ohms)resistance,I4    =", I4," A"
print  "total  resistance,R  =  ", R," ohm"
print  "voltage  drop  across  r5(3  ohms)  resistance,V1  =", V1," volts"
print  "voltage  drop  across  section  ABC,V2  =  ", V2," volts"
print  "voltage  drop  across  r3  resistance(8.8  ohms),V3  =  ",V3," Volts"
print  "  voltage  drop  between  section  AB,V4  =  ", V4,"volts"

current  flowing  through  r1  (2  ohms)  resistance,I3  = 9.0  A
current  flowing  through  r2  (3  ohms)resistance,I4    = 6.0  A
total  resistance,R  =   8.0  ohm
voltage  drop  across  r5(3  ohms)  resistance,V1  = 90.0  volts
voltage  drop  across  section  ABC,V2  =   150.0  volts
voltage  drop  across  r3  resistance(8.8  ohms),V3  =   132.0  Volts
  voltage  drop  between  section  AB,V4  =   18.0 volts

Example 3.10: Page 54

In [10]:
from __future__ import division
import math

#given  data  :
I=44;#  current  in  A
r1=6;#  resistance  in  ohm
r2=12;#  resistance  in  ohm
r3=18;#  resistance  in  ohmr1

# calculation:
a=(1/r1)+(1/r2)+(1/r3);
R=1/a;
V=I*R;
i1=V/r1;
i2=V/r2;
i3=V/r3;

#Results
print  "current  in  6  ohm  resistance,i1  =  ",i1,"A" 
print  "current  in  12  ohm  resistance,i2 =  ",i2,"A"
print  "current  in  18  ohm  resistance,i3 =  ",i3,"A"

current  in  6  ohm  resistance,i1  =   24.0 A
current  in  12  ohm  resistance,i2 =   12.0 A
current  in  18  ohm  resistance,i3 =   8.0 A

Example 3.11: Page 55

In [7]:
from __future__ import division
import math

#given:
t=15  #TOTAL  CURRENT  IN  AMPERES
i1=2  #CURRENT  THROUGH  UNKNOWN  RESISTANCE
R1=15#in  ohms
R2=50/2#in  ohms

# calculations:
x=(t-i1)*((R1*R2)/(R1+2*R2))#unknown  resistance  in  ohms)
PD=i1*x#in  volts
RX=((1/R1)+(1/(2*R2))+(1/x))#
R=1/RX
i5=  PD/(2*R2)#current  in  5  ohms  resistance
i15=PD/R1#current  in  15  ohms  resistance


#Results
print  "(a)unknown  resistance  in  ohms =", x
print  "(b)potential  drop  across  the  circuit  in  volts  is =", PD
print  "(c)current  in  5  ohms  resistance  in  ampere =",i5,"\n and current  in  15  ohms  resistance  in  ampere =", i15
print  "(d)total  resistance  of  the  circuit  in  ohms =",R

(a)unknown  resistance  in  ohms = 75.0
(b)potential  drop  across  the  circuit  in  volts  is = 150.0
(c)current  in  5  ohms  resistance  in  ampere = 3.0 
 and current  in  15  ohms  resistance  in  ampere = 10.0
(d)total  resistance  of  the  circuit  in  ohms = 10.0