Chapter 26
Current and Resistance
In this chapter we will introduce the following new concepts:
-Electric current ( symbol i )
-Electric current density vector (symbol J )
-Drift speed (symbol vd )
-Resistance (symbol R ) and resistivity (symbol ρ ) of a conductor
-Ohmic and non-Ohmic conductors
We will also cover the following topics:
-Ohm’s law
-Power in electric circuits
(26-1)
dq
i
dt
Consider the conductor shown in the figure.
It is connected to a battery (not shown) and
thus charges move through the conductor.
Consider one of the cross sections through
the conductor ( aa or bb or cc ).
dq
The electric current i is defined as i  .
dt
Current = rate at which charge flows
Current SI Unit: C/s, known as the "ampere"
conductor
v
+q
i
conductor
v
-q
i
Current Direction
An electric current is represented by an arrow, which has
the same direction as the charge velocity. The sense of the
current arrow is defined as follows:
1. If the current is due to the motion of positive charges,
the current arrow is parallel to the charge velocity v .
2. If the current is due to the motion of negative charges,
the current arrow is antiparallel to the charge velocity v .
(26-3)
conductor
v A
+q
i
J
conductor
v A
-q
i
i
J
A
J
Current Density
Current density is a vector that is defined as follows:
i
Its magnitude is J 
SI unit for J : A / m2
A
The direction of J is the same as that of the current.
The current through a conductor of cross-sectional
area A is given by the equation i  JA
if the current density is constant.
If J is not constant, then i   J  dA.
We note that even though the current density is a vector
the electric current is not. This is illustrated in the
figure to the left. An incoming current i0 branches at
point a into two currents, i1 and i2 .
Current i0  i1  i2 . This equation expresses the
conservation of charge at point a. Please note
that we have not used vector addition.
(26-4)