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Current, resistance and EMF
8
Theory of Metallic Conduction
�
a =
�
F
m=
q�
E
m, �
v =�
v0
+�
aτ
�
vav
=�
v0 ave
+�
aτ =qτ
m
�
E = σ E
� ����� �����
⇒�
vav
=�
vd
=qτ
m
�
E
⇒�
J = nq�
vd
=nq2τ
m
�
E
⇒ ρ =E
J=
m
nq2τ
=m
ne2τ
.
Average velocity
of an electron
Mean free time:
average time
between collisionsWithout electric field, the
average velocity of an electron
Is zero
9
E
+
�
v0
�
v0
+�
aτ�
v1
�
v1+�
aτ
�
v2
�
v2
+�
aτ
�
v3
�
v3+�
aτ
�
v4
�
v4
+�
aτ
�
vi: velocity after collision�
vi
i
∑ = 0
Drift velocity
Displacement = 2�
vi+�
aτ
2τ
i
∑ =1
2
�
aτ 2N
=1
2
�
aτ (Nτ ) =1
2
�
aτ∆t
⇒�
vd
=1
2
�
aτ
No. of collisions
Direct-current circuits
Resistors in series
• the current must be SAME in all resistors
• The equivalent resistance:
Resistors in parallel
• the potential difference (voltage) must be SAME across
all resistors
• The equivalent resistance:
4 different ways to connect 3 resistors
Ans. E
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