# Chapter 6 Current electricity¶

## Example 6.1 Page no 191¶

In [3]:
#Given
I=300*10**-3
e=1.6*10**-19                         #C
t=60                                  #S

#Calculation
q=I*t
n=q/e

#Result
print"Number of electron passed is", n

Number of electron passed is 1.125e+20


## Example 6.2 Page no 191¶

In [7]:
#Given
e=1.6*10**-19                          #C
v=6.8*10**15                            #revolution/s
r=0.51*10**-10                            #m

#Calculation
I=e*v

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

Equivalent current is 1.088 *10**-3 A


## Example 6.3 Page no 191¶

In [13]:
#Given
I=10                 #A
n=9*10**28           #/m**3
A=10.0**-4              #m**2
e=1.6*10**-19

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

#Result
print"Drift velocity is", round(Vd*10**6,2)*10**-6,"m/s"

Drift velocity is 6.94e-06 m/s


## Example 6.4 Page no 191¶

In [22]:
#Given
n=8.5*10**28                          #/m**3
I=3                                   #A
A=2.0*10**-6                          #m**2
l=3                                   #m
e=1.6*10**-19

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

#Result
print"Drift velocity of the electron is", round(Vd*10**4,3),"*10**-4 m/s"

Drift velocity of the electron is 1.103 *10**-4 m/s


## Example 6.5 Page no 191¶

In [30]:
#Given
A=10**-7                    #m**2
I=1                         #A
K=6.023*10**23
w=63.5
d=9*10**3                      #Kg/m**3

#Calculation
a=(K/w)*1000
n=a*d
Vd=I/(n*e*A)

#Result
print"Average drift velocity is", round(Vd*10**4,2),"*10**-4 m/s"

Average drift velocity is 7.32 *10**-4 m/s


## Example 6.6 Page no 191¶

In [34]:
#Given
V=5                     #Volt
l=0.1                     #m
vd=2.5*10**-4               #m/s

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

#Result
print"Electron mobility is", u,"m**2/V/s"

Electron mobility is 5e-06 m**2/V/s


## Example 6.7 Page no 191¶

In [37]:
#Given
V=3                    #Volt
l=0.2                  #m
A=10**-6                #m**2
n=8.5*10**28              #/m**3
u=4.5*10**-6                #m**2/V/s
e=1.6*10**-19

#Calculation
E=V/l
I=n*A*u*E*e

#Result
print"Current through the wire is",round(I,2),"A"

Current through the wire is 0.92 A


## Example 6.8 Page no 191¶

In [45]:
#Given
I=1.8                #A
A=0.5*10**-6              #m**2
n=8.8*10**28
e=1.6*10**-19

#Calculation
j=I/A
vd=j/(n*e)

#Result
print"Drift velocity is", round(vd*10**4,2),"*10**-4 m/s"

Drift velocity is 2.56 *10**-4 m/s


## Example 6.9 Page no 192¶

In [53]:
#Given
V=1.5                              #V
n=8.4*10**28                       #/m**3
l=0.2                                #m
A=0.3*10**-6                        #m**2
I=2.4                               #A
m=9.1*10**-31                       #Kg
e=1.6*10**-19

#Calculation
E=V/l
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 6.10 Page no 192¶

In [55]:
#Given
V=200                 #V
R=100.0                  #ohm
t=1

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

#Result
print"Number of electrons is", n

Number of electrons is 1.25e+19


## Example 6.11 Page no 192¶

In [62]:
#Given
R=2                         #ohm
l=1                         #m
d=4*10**-4                     #m

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

#Result
print"Resistivity of the material is", round(a*10**7,3)*10**-7,"ohm m"

Resistivity of the material is 2.513e-07 ohm m


## Example 6.12 Page no 192¶

In [76]:
#Given
m=0.45                #Kg
R=0.14                #ohm
a=1.78*10**-8              #ohm m
l=1.99
d=8.93*10**3

#Calculation
import math
l=(math.sqrt(R*m/(a*d)))/10.0
r=math.sqrt(m/(math.pi*l*d))

#Result
print"Length is", round(l,2),"m"

Radius is 2.84 mm
Length is 1.99 m


## Example 6.13 Page no 192¶

In [78]:
#Given
R=5

#Calculation
R1=4*R

#Result
print"New resistance is",R1,"ohm"

New resistance is 20 ohm


## Example 6.14 Page no 192¶

In [82]:
#Given
l=3
A=0.02*10**-6                      #m**2
R=2                                 #ohm

#Calculation
a=l/(R*A)

#Result
print"Electrical conductivity is", a*10**-7,"*10**7 S/m"

Electrical conductivity is 7.5 *10**7 S/m


## Example 6.15 Page no 193¶

In [92]:
#Given
V=1.8                     #V
I=1.2                       #A
l=3                          #m
A=5.4*10**-6                       #m**2

#Calculation
R=V/I
G=1/R
a=l/(R*A)

#Result
print"Conductance is",round(G,2),"S"
print"Conductivity is", round(a*10**-5,1),"*10**5 S/m"

Conductance is 0.67 S
Conductivity is 3.7 *10**5 S/m


## Example 6.16 Page no 193¶

In [99]:
#Given
R1=2.1                  #ohm
a1=300.0                   #K
a2=373.0
R2=2.7                    #ohm

#Calculation
A=(R2-R1)/(R1*(a2-a1))

#Result
print"Temperature coefficient is", round(A*10**3,3),"*10**-3 /K"

Temperature coefficient is 3.914 *10**-3 /K


## Example 6.17 Page no 193¶

In [110]:
#Given
a1=50                           #degree
R1=6.0                           #ohm
a2=100                          #degree
R=7                             #ohm

#Calculation
a=(R-R1)/(R1*(a2-a1))
R0=R1/(1+(a*a1))

#Result
print"Mean temperature coefficient is", round(a,4),"degree/C"
print"Resistance of the conductor is",round(R0,3),"W"

Mean temperature coefficient is 0.0033 degree/C
Resistance of the conductor is 5.143 W


## Example 6.18 Page no 193¶

In [117]:
#Given
V=230                       #v
a=27                        #degree C
I1=3.2                       #A
I2=2.8                        #A
a1=1.70*10**-4                   #degree/C

#Calculation
R1=V/I1
R2=V/I2
a2=a+((R2-R1)/(R1*a1))

#Result

Steady temperature is 867.34 degree C


## Example 6.21 Page no 193¶

In [125]:
#Given
R1=1                         #ohm
R2=2
R3=3
E=12                          #V

#Calculation
Rs=R1+R2+R3
I=E/Rs
R11=I*R1
R12=I*R2
R13=I*R3

#Result
print"(a) Total resistance of the combination is",Rs,"ohm"
print"(b) Potential drop across R1 is",R11,"V"
print" Potential drop across R2 is",R12,"V"
print" Potential drop across R3 is",R13,"V"

(a) Total resistance of the combination is 6 ohm
(b) Potential drop across R1 is 2 V
Potential drop across R2 is 4 V
Potential drop across R3 is 6 V


## Example 6.22 Page no 193¶

In [134]:
#Given
R1=2.0                  #ohm
R2=4.0                  #ohm
R3=5.0
E=20                         #V

#calculation
Rp=1/(1/R1+1/R2+1/R3)
I=E/Rp
I1=E/R1
I2=E/R2
I3=E/R3

print"(a) Toatl resisatnce is", round(Rp,2),"ohm"
print"(b) Current through R1 is",I1,"A"
print"Current through R2 is",I2,"A"
print"Current through R3 is",I3,"A"

(a) Toatl resisatnce is 1.05 ohm
(b) Current through R1 is 10.0 A
Current through R2 is 5.0 A
Current through R3 is 4.0 A


## Example 6.24 Page no 194¶

In [135]:
#Given
R=6
R1=2.0

#calculation
n=R/R1

#Result
print"Number of resistance is",n

Number of resistance is 3.0


## Example 6.25 Page no 194¶

In [141]:
#Given
R1=9.0                 #ohm
R2=5.0
R3=3.0
R4=7.0

#Calculation
R11=R1+R2
R22=R3+R4
R=1/(1/R11+1/R22+1/R22)

#Result
print"Equivalent resistance is",round(R,2),"ohm"

Equivalent resistance is 3.68 ohm


## Example 6.26 Page no 194¶

In [148]:
#Given
R1=3                      #ohm
R2=3

#Calculation
R11=R1+R2
R22=(R11*R11)/(R11+R11)
R=R11*R1/(R11+R1)

#Result
print"Effective resistance is", R,"ohm"

Effective resistance is 2 ohm


## Example 6.27 Page no 195¶

In [151]:
#Given
R1=30.0                  #ohm
R2=30.0
E=2                    #V

#Calculation
R11=R1+R2
R=R11*R1/(R11+R1)
I=E/R

#Result
print"Current through the cell is",I,"A"

Current through the cell is 0.1 A


## Example 6.28 Page no 195¶

In [165]:
#Given
Rl=500.0                          #ohm
E=50                            #V
Rac=2000.0                       #ohm
Rab=500.0

#Calculation
Rbc=Rac-Rab
R11=1/(1/Rbc+1/Rl)
I=E/(Rab+R11)
V=E-(I*Rab)
I1=E/Rac
Rbc1=40/I1

#Result
print"(a) Potential difference across the load is", round(V,2),"V"
print"(b) Resistance is",Rbc1,"ohm"

(a) Potential difference across the load is 21.43 V
(b) Resistance is 1600.0 ohm


## Example 6.29 Page no 195¶

In [169]:
#Given
R1=3                         #ohm
E=9                         #V

#Calcuation
R=R1+R1+R1
I=E/R
I1=I/4.0

#Result
print"Total resistance is",R,"ohm"
print"Current is",I1,"A"

Total resistance is 9 ohm
Current is 0.25 A


## Example 6.30 Page no 196¶

In [174]:
#Given
R1=1                            #ohm
R2=1
r=2/3.0                              #ohm
E=1                                   #V

#Calculation
R11=R1*R2/(R1+R2)
R=1/(1/R1+1/R2+1/R1)
I=E/(R+r)

#Result
print"Current drawn from the cell is", I,"A"

Current drawn from the cell is 1.5 A


## Example 6.31 Page no 196¶

In [199]:
#Given
R=10.0                         #ohm
r=3.33
E=15

#Calculation
Rp=1/(1/R+(1/(R+R)))
R1=R+Rp+R
I=E/(R1+r)
V=I*Rp
I1=V/(R+R)
I2=V/R

#Result
print"Current flow through the main circuit is", round(I,1),"A"
print"Current through QRS is",round(I1,3),"A"
print"Current through QS is",round(I2,3),"A"

Current flow through the main circuit is 0.5 A
Current through QRS is 0.167 A
Current through QS is 0.333 A


## Example 6.32 Page no 196¶

In [206]:
#Given
R1=2                          #ohm
R2=3
R3=2.8
E=6                          #V

#calculation
R=(R1*R2/(R1+R2))+R3
I=E/R

#Result
print"Current in steady state is", round(I,1),"A"

Current in steady state is 1.6 A


## Example 6.33 Page no 197¶

In [212]:
#Given
E=10                     #v
r=3                       #ohm
I=0.5                       #A

#Calculation
R=(E/I)-r
V=I*R

#Result
print"Resistance of the resistor is", R,"ohm"
print"Terminal voltage is",V,"V"

Resistance of the resistor is 17.0 ohm
Terminal voltage is 8.5 V


## Example 6.35 Page no 197¶

In [7]:
#Given
R1=3.0                        #ohm
R2=4.0
R3=6.0
r=2/3.0
E=2                             #V

#Calculation
Rp=1/(1/R1+1/R2+1/R3)
R=Rp+r
I=E/R
V=I*Rp
I1=V/R1

#Result
print"Current drawn from the cell is", I,"A"
print"Current through 3 Ohm resistance is",round(I1,2),"A"

Current drawn from the cell is 1.0 A
Current through 3 Ohm resistance is 0.44 A


## Example 6.36 Page no 197¶

In [11]:
#Given
E=8
R=3.0
r=1.0

#Calculation
I=E/(R+r)
I1=I/2.0

#Result
print"Current from the battery is",I,"A"
print"Current through AC and ABC is",I1,"A"

Current from the battery is 2.0 A
Current through AC and ABC is 1.0 A


## Example 6.37 Page no 198¶

In [17]:
#Given
E=12                     #V
R2=8                       #ohm
r=1                          #ohm

#Calculation
R1=-((E/I)-R2-r)

#Result
print"Value of resistance is", R1,"ohm"

Value of resistance is 3.0 ohm


## Example 6.38 Page no 198¶

In [34]:
#Given
E1=20                         #V
r1=1                            #ohm
E2=8                             #Volt
r2=2                             #ohm
R1=12.0
R2=6.0
R3=4.0

#Calculation
E=E1-E2
R11=1/(1/R1+1/R2+1/R3)
R=R11+r1+r2+5
I=E/R
I1=I-1
V1=E1-(I*r1)
V2=E2+(I*r2)

#Result
print"(a) Current in the circuit is", I,"A"
print"(b) Current in the resister is", I1,"A"
print"(c) Potential difference across 12 V battery is", V1,"V"
print"    Potential difference across 8 V battery is",V2,"V"

(a) Current in the circuit is 1.2 A
(b) Current in the resister is 0.2 A
(c) Potential difference across 12 V battery is 18.8 V
Potential difference across 8 V battery is 10.4 V


## Example 6.39 Page no 198¶

In [41]:
#Given
E=2                          #V
r=0.015                       #ohm
R=8.5

#Calculation
E1=E*6
r1=r*6
I=E1/(R+r1)
V=I*R

#Result
print"Current drawn from the supply is", round(I,3),"A"
print"Terminal voltage is",round(V,3),"V"

Current drawn from the supply is 1.397 A
Terminal voltage is 11.874 V


## Example 6.40 Page no 198¶

In [48]:
#Given
E=4                #V
I=1.5             #A
R=6                 #ohm

#Calculation
E1=3*E
r=((E1/I)-R)/3.0
V=E-(I*r)

#Result
print"(a) Internal resistance is", round(r,2),"ohm"
print"(b) Terminal voltage is",V,"Volt"

(a) Internal resistance is 0.67 ohm
(b) Terminal voltage is 3.0 Volt


## Example 6.41 Page no 199¶

In [53]:
#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 resistance is", r,"ohm"

Internal resistance is 7.5 ohm


## Example 6.42 Page no 199¶

In [66]:
#Given
E=1
a=2

#Calculation
r=(a*E*(a-E))/(a*E*(a-E))

#Result
print"The internal resistance is",r,"ohm"

The internal resistance is 1 ohm


## Example 6.43 Page no 199¶

In [63]:
#Given
E=2              #V
r=1.5            #ohm
R=10             #ohm
r1=1.5
r2=1.5

#Calculation
E1=2*E
w=r1+r2
A=1/(1/w+1/w)
B=R+A
I=E1/B
IR=I*R

#Result
print"The potential difference across external resistance is",round(IR,2),"V"

The potential difference across external resistance is 3.48 V


## Example 6.44 Page no 200¶

In [73]:
#Given
n=2.7*10**18
N=1.0*10**18
e=1.6*10**-19
V=230                  #V

#Calculation
I=(n+N)*(e)
R=V/I

#Result
print"The effective resistance of the tube is",round(R,1),"ohm"

The effective resistance of the tube is 388.5 ohm


## Example 6.47 Page no 200¶

In [99]:
#Given
X=1
a=3
E1=12
r=0.5

#Calculation
import math
X1=X+math.sqrt(a)
I=E1/(X1+r)

#Result
print"Current drawn is", round(I,3),"A"

Current drawn is 3.713 A


## Example 6.48 Page no 200¶

In [91]:
#Given
R1=6
R2=3.0
R3=5
E=24              #V
I=3               #A

#Calculation
Rp=(R1*R2)/(R1+R2)
R=R3+Rp+r
r=R-(R3+Rp)
V=I*Rp
I1=V/R1
I2=V/R2
R11=R2+R3+r
I11=E/R11

#Result
print"(a) Internal resistance is", r,"ohm"
print"   Current I1 is",I1,"A and I2 is",I2,"A"
print"(b) Current in the circuit is",round(I11,2),"A"

(a) Internal resistance is 1.0 ohm
Current I1 is 1.0 A and I2 is 2.0 A
(b) Current in the circuit is 2.67 A