# Chapter 5 Electric current and resistance¶

## Example 5.1 Page no 257¶

In [5]:
#Given
n=10**17
e=1.6*10**-19               #C
t=1.0                       #S

#Calculation
I=n*e/t

#Result
print"The magnitude of current in the wire is ",I*10**2,"10**-2 A and direction is from left to right"

The magnitude of current in the wire is  1.6 10**-2 A and direction is from left to right


## Example 5.2 Page no 257¶

In [21]:
#given
I=0.5
T=1
e=1.6*10**-19
t=60               #minute

#Calculation
n=I*T/e
q=I*t**2
n1=q/e

#Result
print"(i) The number of electrons passing a cross section of the bulb is ",round(n*10**-18,1)*10**18,"electrons/S"
print"(ii) The number of electrons is ",round(n1*10**-22,1)*10**22,"electrons/hour"

(i) The number of electrons passing a cross section of the bulb is  3.1e+18 electrons/S
(ii) The number of electrons is  1.1e+22 electrons/hour


## Example 5.3 Page no 257¶

In [25]:
#Given
e=1.6*10**-19                  #C
f=6.8*10**15                   #rev/sec
r=0.51*10**-10                  #m

#Calculation
I=e*f

#Result
print"The equivalent current is ", I*10**3,"*10**-3 A"

The equivalent current is  1.088 *10**-3 A


## Example 5.5 Page no 267¶

In [28]:
#Given
I=10              #A
A=1               #m*m**2
e=1.6*10**-19         #C
n=10**28              #m**-3

#Calculation
Vd=I/(n*A*e)

#Result
print"Drift velocity of the conduction electrons are ", Vd,"m/s"

Drift velocity of the conduction electrons are  6.25e-09 m/s


## Example 5.6 Page no 267¶

In [35]:
#Given
I=10                #A
A=4*10**-6                 #m**2
e=1.6*10**-19                #C
n=8*10**28                     #m**-3
l=4

#Calculation
Vd=I/(n*A*e)
t=l/Vd

#Result
print"Time required by an electron is ", t*10**-4,"*10**4 S"

Time required by an electron is  2.048 *10**4 S


## Example 5.7 page no 267¶

In [53]:
#Given
a=6.023*10**23
m=63.5*10**-3
d=9*10**3
A=10**-7                   #m**2
e=1.6*10**-19                   #C
I=1.5                           #a
K=1.38*10**-23                 #J/K
T=300                           #K
Vd=1.1*10**-3
C=3*10**8

#Calculation
import math
n=a*d/m
Vd=I/(n*A*e)
V=math.sqrt((3*K*T*a)/m)
V1=Vd/V
E=Vd/C

#Result
print"(i) Thermal speeds of copper atoms at ordinary temperatures are ", round(V1*10**6,2),"*10**-6 m/s"
print"(ii) Speed of propagation of electric fild is ", round(E*10**12,1)*10**-12

(i) Thermal speeds of copper atoms at ordinary temperatures are  3.2 *10**-6 m/s
(ii) Speed of propagation of electric fild is  3.7e-12


## Example 5.8 Page no 268¶

In [57]:
#Given
V=5
l=0.1
Vd=2.5*10**-4

#Calculation
E=V/l
u=Vd/E

#Result
print"The electron mobility is ", u,"m**2/V/C"

The electron mobility is  5e-06 m**2/V/C


## Example 5.9 Page no 268¶

In [64]:
#Given
I=2.4
A=0.30*10**-6
m=9.1*10**-31
n=8.4*10**28
e=1.6*10**-19
E=7.5

#Calculation
J=I/A
t=m*J/(n*e**2*E)

#Result
print"Average relaxation time is ", round(t*10**16,2)*10**-16,"S"

Average relaxation time is  4.51e-16 S


## Example 5.10 Page no 268¶

In [82]:
#Given
r=0.12*10**-2                 #m
I=10
r1=0.08*10**-2                    #m
I=10                                  #A
e=1.6*10**-19                                  #C
n=8.4*10**28

#Calculation
import math
A=math.pi*(r**2)
J=I/A
A1=math.pi*r1**2
Vd=I/(e*n*A1)

#Result
print"(i) Current density in the alluminium wire is ",round(J*10**-6,1),"*10**6 A/m**2"
print"(ii) Drift velocity of electrons in the copper wire is ",round(Vd*10**4,1),"*10**-4 m/S"

(i) Current density in the alluminium wire is  2.2 *10**6 A/m**2
(ii) Drift velocity of electrons in the copper wire is  3.7 *10**-4 m/S


## Example 5.11 Page no 269¶

In [93]:
#Given
D=0.13*10**-2
R=3.4                       #ohms
l=10.0

#Calculation
import math
A=(math.pi/4.0)*D**2
a=R*A/l
b=1/a

#Result
print"Conductivity of a material is ",round(b*10**-6,1),"*10**6 S/m"

Conductivity of a material is  2.2 *10**6 S/m


## Example 5.12 Page no 269¶

In [98]:
#Given
A1=25.0                            #mm**2
l2=1                             #m
R2=1/58.0
A2=1
l1=1000

#Calculation
R=(l1/l2)*(A2/A1)
R1=R*R2

#Result
print"The value of resistance is ", round(R1,2),"ohm"

The value of resistance is  0.69 ohm


## Example 5.13 Page no 269¶

In [103]:
#Given
R1=4.5
A1=1
A2=2.0
l2=3
l1=1.0

#Calculation
R=(l2/l1)*(A1/A2)
R2=R*R1

#Result
print"The resistance of another wire is ", R2,"ohm"

The resistance of another wire is  6.75 ohm


## Example 5.14 Page no 269¶

In [115]:
#Given
r=1
r1=0.5
R1=0.15                    #ohm

#Calculation
import math
A1=(math.pi/4.0)*r**2
A2=(math.pi/4.0)*r1**2
l=A1/A2
R=l*l
R2=R*R1

#Result
print"New resistance of the wire is ", R2,"ohm"

New resistance of the wire is  2.4 ohm


## Example 5.15 Page no 270¶

In [118]:
#Given
R=1.5                         #ohm
e=1.6*10**-19                  #C
t=1                          #second
V=3                           #V

#Calculation
I=V/R
n=I*t/e

#Result
print "Number of electrons flowing through it in 1 S is ",n

Number of electrons flowing through it in 1 S is  1.25e+19


## Example 5.16 Page no 270¶

In [124]:
#Given
ne=2.8*10**18
np=1.2*10**18
e=1.6*10**-19
t=1                             #S
V=220

#Calculation
q=(ne+np)*e
I=q/t
R=V/I

#Result
print"Effective resistance of the tube is ", round(R,0),"ohm"

Effective resistance of the tube is  344.0 ohm


## Example 5.17 Page no 270¶

In [130]:
#Given
m=84                      #g
d=10.5                    #g/cm**3
a=1.6*10**-6

#Calculation
V=m/d
s=V**(1/3.0)
R=a/2.0

#Result
print"Resistance between the opposite faces is ", R,"ohm"

Resistance between the opposite faces is  8e-07 ohm


## Example 5.18 Page no 270¶

In [137]:
#Given
l=1.001
A=1.001

#Calculation
R=l*A
R1=R-1
A=R1*100

#Result
print"Percentage change in its resistance is ", round(A,1),"%"

Percentage change in its resistance is  0.2 %


## Example 5.19 Page no 271¶

In [148]:
#Given
m=0.45                         #Kg
R=0.0014                        #ohm
a=1.78*10**-8                   #ohm
d=8.93*10**3                       #Kg/m**3

#Calculation
import math
l=math.sqrt(R*m/(a*d))
r=math.sqrt(m/(math.pi*d*1.99))

#Result
print"The value of length is",round(l,2),"m"
print"The value of radius is ",round(r*10**3,2),"mm"

The value of length is 1.99 m
The value of radius is  2.84 mm


## Example 5.20 Page no 271¶

In [154]:
#Given
R15=80                    #ohm
a=0.004

#Calculation
R0=R15/(1+15*a)
R50=R0*(1+a*50)

#Result
print"The value of resistance at 50 degree C is ", round(R50,2),"ohm"

The value of resistance at 50 degree C is  90.57 ohm


## Example 5.21 Page no 271¶

In [160]:
#Given
R20=20                         #ohm
P=60                            #W
V=120.0                           #Volts
a=5*10**-3

#Calculation
I=P/V
Rt=V/I
t=(((Rt/R20)-1)/a)+R20

#Result
print"Normal working temperature of the lamp is ", t,"degree C"

Normal working temperature of the lamp is  2220.0 degree C


## Example 5.22 Page no 271¶

In [165]:
#Given
R0=5                    #ohm
R100=5.23                  #ohm
Rt=5.795                   #ohm

#Calculation
t=((Rt-R0)/(R100-R0))*100

#Result
print"The temperature of the bath is ", round(t,2),"degree C"

The temperature of the bath is  345.65 degree C


## Example 5.23 Page no 272¶

In [172]:
#Given
A=15*10**-4                         #m**2
a=7.6*10**-8                                # ohm m
l=2000                              #m
b=0.005                          #degree/C

#Calculation
R0=a*l/A
R50=R0*(1+(b*50))

#Result
print"The value of resistance is ", round(R50,3),"ohm"

The value of resistance is  0.127 ohm


## Example 5.24 Page no 272¶

In [175]:
#Given
a=0.004
ac=0.0007
R0=100

#Calculation
R=ac*R0/a

#Result
print"The resistance of a copper filament is ", R,"ohm"

The resistance of a copper filament is  17.5 ohm


## Example 5.28 Page no 281¶

In [178]:
#Given
R1=4.0                     #ohm
R2=4.0                     #ohm

#Calculation
Rab=1/((1/R1)+(1/R2))

#Result
print"The equivalent resisatance is ", Rab,"ohm"

The equivalent resisatance is  2.0 ohm


## Example 5.29 Page no 281¶

In [181]:
#Given
R1=15                    #ohm
R2=30                   #ohm

#Calculation
R=R1*R2/(R1+R2)

#Result
print"The equivqlent resistance between A and B is ", R,"ohm"

The equivqlent resistance between A and B is  10 ohm


## Example 5.31 Page no 282¶

In [187]:
#Given
R1=5                 #ohm
R2=9                  #ohm
R3=14                  #ohm
R4=11
R5=7
R6=18
R7=13
R8=22
V=22

#Calculation
Rec=(R1+R2)*R3/(R1+R2+R3)
Rbe=(R4+R5)*R6/(R4+R5+R6)
Rae=(R7+R2)*R8/(R7+R2+R8)
I=V/Rae

#Result
print"The value of current in the branch AF is ", I,"A"

The value of current in the branch AF is  2 A


## Example 5.32 Page no 282¶

In [191]:
#Given
R1=12                     #ohm
R2=6                      #ohm

#Calculation
Rdg=R1*R2/(R1+R2)
Rch=R1*R2/(R1+R2)
Rab=Rdg+Rch

#Result
print"The equivalent resistance is ", Rab,"ohm"

The equivalent resistance is  8 ohm


## Example 5.33 Page no 283¶

In [206]:
#Given
Rab=500.0                      #ohm
Rl=500                        #ohm
Rbc=1500                      #ohm
E=50                          #Volts
Rac=2000.0                      #ohm
V=40

#Calculation
R=Rbc*Rl/(Rbc+Rl)
I=E/(Rab+R)
Pd=I*Rab
Rl1=E-Pd
I1=E/Rac
R12=V/I1

#Result
print"(i) Potential difference across the road is ", round(Rl1,2),"V"
print"(ii) Resistance at BC is ", R12,"ohm"

(i) Potential difference across the road is  21.43 V
(ii) Resistance at BC is  1600.0 ohm


## Example 5.35 Page no 284¶

In [210]:
#Given
R1=5                        #ohm
R2=5.0                       #ohm
R=6

#Calculation
n=(1/(R-R1)*R2)

#Result
print"There are", n,"resistance are in parallel"

There are 5.0 resistance are in parallel


## Example 5.36 Page no 284¶

In [218]:
#Given
R1=20.0                       #ohm
R2=10.0                        #ohm
R4=10

#Calculation
Rbd=(R1*R2)/(R1+R2)
Rae=R2+Rbd+R4

#Result
print"The value of resistance is ", round(Rae,2),"ohm"

The value of resistance is  26.67 ohm


## Example 5.37 Page no 284¶

In [226]:
#Given
R1=2.0                     #ohm
R2=3                         #ohm
R3=2.8
E=6                              #V

#Calculation
Rab=R1*R2/(R1+R2)
Rt=Rab+R3
I=E/Rt
Vab=I*Rab
I1=Vab/2.0

#Result
print"The steady state current is ", I1,"A"

The steady state current is  0.9 A


## Example 5.38 Page no 285¶

In [234]:
#Given
R1=3                 #ohm
R2=3
R3=6

#Calculation
Raf=(Rae+R1)*R3/(Rae+R1+R3)
Rab=(Raf+R1)*R2/(Rae+R1+R2)

#Result
print"the effective resistance between the point A and B is", Rab,"Ohm"

the effective resistance between the point A and B is 2 Ohm


## Example 39 Page no 285¶

In [251]:
#Given
R2=50.0                     #ohm
R3=50.0                       #ohm
R4=75.0                       #ohm
E=4.75
R1=100

#Calculation
Rbc=1/((1/R2)+(1/R3)+(1/R4))
R=R1+Rbc
I=E/R
R11=I*R1
Vbc=E-(I*R1)
I2=Vbc/R2
I3=Vbc/R3
I4=Vbc/R4

#Result
print"Equivalent resistance of the circuit is ", R,"ohm"
print"Current in R2 is",I2,"A"
print"Current in R3 is",I3,"A"
print"Current in R4 is",I4,"A"

Equivalent resistance of the circuit is  118.75 ohm
Current in R2 is 0.015 A
Current in R3 is 0.015 A
Current in R4 is 0.01 A


## Example 5.40 Page no 292¶

In [254]:
#Given
V=19
I1=0.5
I2=2                       #A
r=2

#Calculation
E=V+I1*r

#Result
print"E.M.F is ", E,"V"

E.M.F is  20.0 V


## Example 5.41 Page no 292¶

In [268]:
#Given
V=1.5
a=1.5
r1=0.5                     #ohm
r2=0.25
R=2.25                      #ohm

#Calculation
E=V+a
r=r1+r2
Rt=r+R
I=E/Rt
pd=V-(I*r1)
pd1=V-(I*r2)

#Result
print"(i) The circuit current is ",I,"A"
print"(ii) P.D across the terminals of each  cell is ",pd,"V and ",pd1,"V"

(i) The circuit current is  1.0 A
(ii) P.D across the terminals of each  cell is  1.0 V and  1.25 V


## Example 5.42 Page no 292¶

In [277]:
#Given
n=10
E=1.5
R=4                     #ohm
r=0.1
a=8

#Calculation
Emf=n*E
Rt=R+(n*r)
I=Emf/Rt
Emf1=(a*E)-(2*E)
I1=Emf1/Rt
I11=I-I1

#Result
print"Reduction in current is ", I11,"A"

Reduction in current is  1.2 A


## Example 5.43 Page no 292¶

In [283]:
#Given
Emf=2
Emf1=1.9
Emf2=1.8
R1=0.05
R2=0.06
R3=0.07
R0=5                   #ohm

#Calculation
Emft=Emf+Emf1+Emf2
R=R1+R2+R3
Rt=R+R0
I=Emft/Rt

#Result
print"The reading of the ammeter is ", round(I,1),"A"

The reading of the ammeter is  1.1 A


## Example 5.44 Page no 293¶

In [295]:
#Given
R1=6.0                #ohm
R2=3
I=0.8                  #A
a=24

#Calculation
I1=I*(R1+R2)/R1
I11=I1-I
Rp=R1*R2/(R1+R2)
Rt=Rp+8
r=(a/I1)-10
V=I1*Rt

#Result
print"(i) Current in 6 ohm resistance is ", I11,"A"
print"(ii) Internal resistance of the battery is ", r,"ohm"
print"(iii) The terminal potential difference of the battery is ", V,"V"

(i) Current in 6 ohm resistance is  0.4 A
(ii) Internal resistance of the battery is  10.0 ohm
(iii) The terminal potential difference of the battery is  12.0 V


## Example 5.45 Page no 294¶

In [299]:
#Given
R1=2               #ohm
R2=4
R3=6
E=8
r=1

#Calculation
Rac=(R1+R2)*R3/(R1+R2+R3)
I=E/(Rac+r)
I1=I/2.0

#Result
print"Internal resistance is ", I1,"A"

Internal resistance is  1.0 A


## Example 5.46 Page no 294¶

In [18]:
#Given
E=1
R=2

#Calculation
r=(E*R)-E
print"The internal resisatnce of aech cell is ",r,"ohm"

The internal resisatnce of aech cell is  1 ohm


## Example 5.47 Page no 294¶

In [6]:
#Given
R1=15.0                          # ohm
R2=15.0
E=2
V=1.6

#Calculation
R=R1*R2/(R1+R2)
r=((E/V)-1)*R*4

#Result
print"Internal resisatnce of each cell is ", r,"ohm"

Internal resisatnce of each cell is  7.5 ohm


## Example 5.48 Page no 295¶

In [20]:
#Given
I1=1                     #A
E=1.5
I2=0.6
R2=2.33                       #ohm

#Calculation
R=2*E/I1
R1=2*E/I2
r=R1-2*R2

#Result
print"Internal resisatnce of each battery is ", r,"ohm"

Internal resisatnce of each battery is  0.34 ohm


## Example 5.49 Page no 295¶

In [46]:
#Given
R1=4                   #ohm
R2=4                            #ohm
R3=12
R4=6.0
E=16
r=1                         #ohm

#calculation
Rab=R1*R2/(R1+R2)
Rcd=R3*R4/(R3+R4)
R=Rab+Rcd+1
I=E/(R+r)
I1=I/2.0
I3=I*R4/(R3+R4)
I4=I*R3/(R3+R4)
Vab=4*I1
Vbc=I*1
Vcd=12*I3

#Result
print"(i) equivalent resistance of the network is ", R,"ohm"
print"(ii) Circuit current is", I,"A , Current in R1 is",I1,"A , Current in R3 is",round(I3,2),"A , Current in R4 is ",round(I4,2)
print "Voltage drop Vab is",Vab,"V \nVbc is",Vbc,"V \nVcd is",Vcd,"V"

(i) equivalent resistance of the network is  7.0 ohm
(ii) Circuit current is 2.0 A , Current in R1 is 1.0 A , Current in R3 is 0.67 A , Current in R4 is  1.33
Voltage drop Vab is 4.0 V
Vbc is 2.0 V
Vcd is 8.0 V