Chapter 31 CURRENT AND RESISTANCE

Example 31.1 Current density

In [1]:
from __future__ import division
import math
d1=0.10 #diameter of aluminium wire in inches
d2=0.064 #diameter of copper wire in inches
i=10 #current carried by composite wire in amperes
A1=math.pi*(d1/2)**2 #crosssectional area of aluminium wire in square inches
A2=math.pi*(d2/2)**2 #crosssectional area of copper wire in square inches
j1=i/A1
j2=i/A2
print("Current density in Aluminium wire in amp/square inches %.3f"%j1)
print("Current density in copper wire in amp/square inches %.3f"%j2)

Current density in Aluminium wire in amp/square inches 1273.240
Current density in copper wire in amp/square inches 3108.495

Example 31.2 Drift speed

In [2]:
from __future__ import division
import math
j=480 #current density for copper wire in amp/cm2
N0=6*10**23 #avagadro number in atoms/mole
M=64 #molecular wt in gm/mole
d=9.0 #density in gm/cm3
e=1.6*10**-19 #elecron charge in coul
n=d*N0/M 
print("No.of free electrons per unit volume in atoms/mole %.3e"%n)
Vd=j/(n*e)
print("Drift speed of electron in cm/sec is %.5f"%Vd)

No.of free electrons per unit volume in atoms/mole 8.438e+22
Drift speed of electron in cm/sec is 0.03556

Example 31.3 Resistance and resistivity

In [5]:
from __future__ import division
import math
print("Dimensions of rectangular carbon block are 1.0cm*1.0cm*50cm")
l=1.0*10**-2 #in meter
b=1.0*10**-2#in meter
h=50*10**-2 #in meter
p=3.5*10**-5 #resisivity of carbon in ohm-m
#(a)Resistance b/w two square ends
l1=h
A1=b*l
R1=p*l1/A1
print("(a) Resistance measured b/w the two square ends in ohm is %.3f"%R1)
l2=l
A2=b*h
R2=p*l2/A2
print("(a) Resistance measured b/w the two opposite rectangular faces in ohm is %.1e"%R2)

Dimensions of rectangular carbon block are 1.0cm*1.0cm*50cm
(a) Resistance measured b/w the two square ends in ohm is 0.175
(a) Resistance measured b/w the two opposite rectangular faces in ohm is 7.0e-05

Example 31.4 Mean time and Mean free path

In [7]:
from __future__ import division
import math
m=9.1*10**-31 #in kg
n=8.4*10**28 #in m-1
e=1.6*10**-19 #in coul
p=1.7*10**-8 #in ohm-m
v=1.6*10**8 #in cm/sec
T=2*m/(n*p*e**2)
print("(a) Mean time b/w collisions in sec is %.3e"%T)
Lambda=T*v
print("(b) Mean free path in cm is %f"%Lambda)

(a) Mean time b/w collisions in sec is 4.979e-14
(b) Mean free path in cm is 0.000008

Example 31.5 Power

In [14]:
from __future__ import division

V=110 #in volt
R=24 #ohms
P1=V**2/R
print("(a)Power for the single coil in watts is %.3f"%P1)
P2=V**2/(R/2)
print("(b)Power for a coil of half the length in watts is %.3f"%P2)

(a)Power for the single coil in watts is 504.167
(b)Power for a coil of half the length in watts is 1008.333