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