A potential difference of 100 V is applied to the
ends of a copper wire one metre long. What is
the average drift velocity of electrons?
(given, sigma = 5.81x10^7 or N cu = 8.5x 10^28 m
(a) 0.43 ms
-1
(b) 0.83 ms -1
(c) 0.52 ms -1
(d) 0.95 ms -1
reis
Answers
Answer:
c is the correct answer!!!
Explanation:
Given,
Potential Difference is 100V
Length of Wire is 1m
Atomic Mass of copper is 63.5g
Density of copper is 9×10
3
N
A
=6.0×10
23
Pergrammole
K=1.38×10
−23
JK
−1
As given one conduction electron per atom therefore Conduction electron density is calculated by,
massofcopper
N
A
×density
Substituting all value in equation
=
63.5
6.0×10
23
×9×10
3
=
63.5
54×10
26
=8.5×10
22
cm
−3
=8.5×10
28
m
−3
Now Electric field is
E=
l
V
=
1
100
=100V/m
We know that Current density is
J=σE=nev
d
Here v
d
is current density
v
d
=σ
ne
E
Substituting all value in above equation
v
d
=
8.5×10
28
×1.61×10
−19
5.81×10
7
×100
=
13.69
5.81
=0.42m/s
And
Thermalvelocity(V
rms
)=
m
e
3K
B
T
=
9.1×10
−31
3×1.38×10
−23
×(273+27)
=116826.16≈1.17×10
5
m/s
Ratio=
ThermalVelocity
DriftVelocity
=
1.17×10
5
0.43
=3.67×10
−6