# Chapter 5: Series and parallel networks

### Example 1, page no. 43

In [1]:
from __future__ import division
#initializing the variables:
V1 = 5; # in volts
V2 = 2; # in volts
V3 = 6; # in volts
I = 4; # in Amperes

#calculation:
Vt = V1 + V2 + V3
Rt = Vt/I
R1 = V1/I
R2 = V2/I
R3 = V3/I

#results
print "(a) Total Voltage", Vt,"Volts(V)"
print "(b)Total Resistance", Rt,"Ohms"
print "(c)Resistance(R1)", R1,"Ohms; Resistance(R2)", R2,"Ohms and"
print "Resistance(R3)", R3,"Ohms"

(a) Total Voltage 13 Volts(V)
(b)Total Resistance 3.25 Ohms
(c)Resistance(R1) 1.25 Ohms; Resistance(R2) 0.5 Ohms and
Resistance(R3) 1.5 Ohms

### Example 2, page no. 43

In [2]:
from __future__ import division
#initializing the variables:
V1 = 10; # in volts
V2 = 4; # in volts
Vt = 25; # in volts
Rt = 100; # in ohms

#calculation:
V3 = Vt - V1 - V2
I = Vt/Rt
R2 = V2/I

#results
print "(a)Voltage(V3)", V3,"Volts(V)"
print "(b)current", I,"Amperes(A)"
print "(c)Resistance(R2)", R2,"Ohms"

(a)Voltage(V3) 11 Volts(V)
(b)current 0.25 Amperes(A)
(c)Resistance(R2) 16.0 Ohms

### Example 3, page no. 44

In [3]:
from __future__ import division
#initializing the variables:
Vt = 12; # in volts
R1 = 4; # in ohms
R2 = 9; # in ohms
R3 = 11; # in ohms

#calculation:
Rt = R1 + R2 + R3
I = Vt/Rt
V9 = I*R2
P11 = I*I*R3
#results
print "a)current", I,"Amperes(A)\n"
print "b)Voltage(V2)", V9,"Volts(V)\n"
print "c)Power", P11,"Watt(W)"

a)current 0.5 Amperes(A)

b)Voltage(V2) 4.5 Volts(V)

c)Power 2.75 Watt(W)

### Example 4, page no. 44

In [4]:
from __future__ import division
#initializing the variables:
Vt = 50; # in volts
R1 = 4; # in ohms
R2 = 6; # in ohms

#calculation:
Rt = R1 + R2
I = Vt/Rt
V2 = I*R2

#results
print "Voltage(V)", V2,"Volts(V)"

Voltage(V) 30.0 Volts(V)

### Example 5, page no. 45

In [5]:
from __future__ import division
#initializing the variables:
Vt = 24; # in volts
R1 = 2; # in ohms
I = 3; # in Amperes
t = 50; # in hrs

#calculation:
V1 = I*R1
R2 = (Vt-(I*R1))/I
E = Vt*I*t

#results
print "a)Voltage(V1)", V1,"Volts(V)\n"
print "b)Resistance(R2)", R2,"Ohms\n"
print "c)Energy(E)", E/1000,"kWh\n"

a)Voltage(V1) 6 Volts(V)

b)Resistance(R2) 6.0 Ohms

c)Energy(E) 3.6 kWh

### Example 6, page no. 46

In [6]:
from __future__ import division
#initializing the variables:
R1 = 5; # in ohms
R3 = 20; # in ohms
I1 = 8; # in Amperes
It = 11; # in Amperes

#calculation:
Vt = I1*R1
I3 = Vt/R3
R2 = Vt/(It - I1 - I3)

#results
print "b)Resistance(R2)", R2,"Ohms\n"

a)Ammeter Reading 2.0 Amperes(A)

b)Resistance(R2) 40.0 Ohms

### Example 7, page no. 46

In [7]:
from __future__ import division
#initializing the variables:
R1 = 3; # in ohms
R2 = 6; # in ohms
Vt = 12; # in volts

#calculation:
Rt = R1*R2/(R1 + R2)
I1 = (Vt/R1)

#Result
print "(a)Total Resistance", Rt,"Ohms\n"
print "(b)Current(I1)", I1,"Amperes(A)\n"

(a)Total Resistance 2.0 Ohms

(b)Current(I1) 4.0 Amperes(A)

### Example 8, page no. 47

In [9]:
from __future__ import division
import math
#initializing  the  variables:
R1  =  10;#  in  ohms
R2  =  20;#  in  ohms
R3  =  60;#  in  ohms
I2  =  3;#  in  Amperes

#calculation:
Vt  =  I2*R2
I1  =  Vt/R1
I3  =  Vt/R3
I  =  I1  +I2  +  I3

print  "\nResult\n"
print  "\n(a)Voltage(V)  ",Vt,"  Volts(V)\n"
print  "\n(b)Total  Current(I)  ",I,"  Amperes(A)\n"

Result

(a)Voltage(V)   60   Volts(V)

(b)Total  Current(I)   10.0   Amperes(A)

### Example 9, page no. 47

In [1]:
from __future__ import division
import math
#initializing  the  variables:
R  =  1;#  in  ohms

#calculation
R1  =  1/(1/R + 1/R + 1/R + 1/R)
R2  =  2*R*2*R/(4*R)
R3  =  1/(1/R + 1/R + 1/R) + 1
R4  =  R*R/(2*R) + 2*R

print  "\n\nResult\n\n"
print  "\n(a)All four in parallel for ",R1,"  ohm\n"
print  "\n(b)Two in series, in parallel with another two in series for",R2,"  ohm\n"
print  "\n(c)Three in parallel, in series with one for ",round(R3,2),"  ohm\n"
print  "\n(d)Two in parallel, in series with two in series for ",R4,"  ohm\n"


Result

(a)All four in parallel for  0.25   ohm

(b)Two in series, in parallel with another two in series for 1.0   ohm

(c)Three in parallel, in series with one for  1.33   ohm

(d)Two in parallel, in series with two in series for  2.5   ohm


### Example 10, page no. 48

In [2]:
from __future__ import division
#initializing  the  variables:
R1  =  1;#  in  ohms
R2  =  2.2;#  in  ohms
R3  =  3;#  in  ohms
R4  =  6;#  in  ohms
R5  =  18;#  in  ohms
R6  =  4;#  in  ohms

#calculation:
R0  =  1/((1/3)  +  (1/6)  +  (1/18))
Rt  =  R1  +  R2  +  R0  +  R6

print  "\n\nResult\n\n"
print  "\n  Equivalent  Resistance  ",Rt,"  Ohms\n"


Result

Equivalent  Resistance   9.0   Ohms

### Example 11, page no. 48

In [15]:
from __future__ import division
import math
#initializing  the  variables:
R1  =  2.5;#  in  ohms
R2  =  6;#  in  ohms
R3  =  2;#  in  ohms
R4  =  4;#  in  ohms
Vt  =  200;#  in  volts

#calculation:
R0  =  1/((1/R2)  +  (1/R3))
Rt  =  R1  +  R0  +  R4
It  =  Vt/Rt
I1  =  It
I4  =  It
I2  =  R3*It/(R3+R2)
I3  =  It  -  I2
V1  =  I1*R1
V2  =  I2*R2
V3  =  I3*R3
V4  =  I4*R4

print  "\n\nResult\n\n"
print  "\n  (a)Total  Current  Supply  ",It,"  Amperes(A)\n"
print  "\n  (b)Current  through  resistors  (R1,  R2,  R3,  R4)\n ",I1,",  ",  I2,",  ",  I3,",  ",  I4,"  Amperes(A)  respectively\n"
print  "\n  (c)voltage  across  resistors  (R1,  R2,  R3,  R4)\n  ",V1,",  ",  V2,",  ",  V3,",  ",  V4,"  Volts(V)  respectively\n"


Result

(a)Total  Current  Supply   25.0   Amperes(A)

(b)Current  through  resistors  (R1,  R2,  R3,  R4)
25.0 ,   6.25 ,   18.75 ,   25.0   Amperes(A)  respectively

(c)voltage  across  resistors  (R1,  R2,  R3,  R4)
62.5 ,   37.5 ,   37.5 ,   100.0   Volts(V)  respectively

### Example 12, page no. 49

In [16]:
from __future__ import division
import math
#initializing  the  variables:
R1  =  15;#  in  ohms
R2  =  10;#  in  ohms
R3  =  38;#  in  ohms
Vt  =  250;#  in  volts
P  =  2500;#  in  Watt

#calculation:
It  =  P/Vt
I2  =  R1*It/(R1+R2)
I1  =  It  -  I2
Re1  =  1/((1/R1)  +  (1/R2))
Rt  =  Vt/It
Re2  =  Rt  -  Re1
Rx  =  1/((1/Re2)  -  (1/R3))
I4  =  R3*It/(R3+Rx)
I3  =  It  -  I4

print  "\n\nResult\n\n"
print  "\n  (a)Resistance  (Rx)  ",Rx,"  Ohms\n"
print  "\n  (b)Current  through  resistors  (R1,  R2,  R3,  R4): \n ",I1,",  ",  I2,",  ",  I3,",  "
print   ",  I4,"  Amperes(A)  respectively\n"


Result

(a)Resistance  (Rx)   38.0   Ohms

(b)Current  through  resistors  (R1,  R2,  R3,  R4):
4.0 ,   6.0 ,   5.0 ,   5.0   Amperes(A)  respectively

### Example 13, page no. 51

In [17]:
from __future__ import division
import math
#initializing  the  variables:
R1  =  8;#  in  ohms
R2  =  2;#  in  ohms
R3  =  1.4;#  in  ohms
R4  =  9;#  in  ohms
R5  =  2;#  in  ohms
Vt  =  17;#  in  volts

#calculation:
R01  =  R1*R2/(R1  +  R2)
R02  =  R01  +  R3
R03  =  R4*R02/(R4  +R02)
Rt  =  R5  +  R03
It  =  Vt/Rt
I1  =  R4*It/(R4  +  R02)
Ix  =  R2*I1/(R1  +  R2)

print  "\n\nResult\n\n"
print  "\n  Current(Ix)  ",Ix,"  Amperes(A)\n"


Result

Current(Ix)   0.6   Amperes(A)

### Example 14, page no. 52

In [18]:
from __future__ import division
import math
#initializing  the  variables:
Rt  =  150;#  in  ohms
n  =  3;#  no.  of  identical  lamp

#calculation:
R  =  Rt*3#  (1/Rt)=(1/R)+(1/R)+(1/R)

print  "\n\nResult\n\n"
print  "\n  Resistance  ",R,"  Ohms\n"


Result

Resistance   450   Ohms

### Example 15, page no. 52

In [21]:
from __future__ import division
import math
#initializing  the  variables:
#series  connection
n  =  3;#  no.  of  identical  lamp
Vt  =  150;#  in  volts

#calculation:
V  =  Vt/3#  Since  each  lamp  is  identical,  then  V  volts  across  each.

print  "\n\nResult\n\n"
print  "\n  a)Voltage  across  each  resistor  =  ",V,"  Volts(V)\n"
print  "\n  b)If  lamp  C  fails,  i.e.,  open  circuits,  no  current  will  flow  and lamps  A  and  B  will  not  operate."


Result

a)Voltage  across  each  resistor  =   50.0   Volts(V)

b)If  lamp  C  fails,  i.e.,  open  circuits,  no  current  will  flow  and lamps  A  and  B  will  not  operate.