Electric Current
• The amount of charge that flows by per unit
time.
• I  Q
t
Steady state
• A system (e.g. circuit) is in the steady state
when the current at each point in the circuit is
constant (does not change with time).
– In many practical circuits, the steady state is
achieved in a short time.
• In the steady state, the charge (or current)
flowing into any point in the circuit has to
equal the charge (or current) flowing out.
– Kirchhoff’s Node (or Current) Rule.
n = number of charges per unit volume = “charge-number density” (n > 1027 m-3 for a
good metal)
Figure 25.26
Typically vd ~ 10-5 m/s ~1 m/day
Why do the electrons have a drift
velocity?
• They feel a force due to an electric field.
• But then they should accelerate!: F = ma
• Each electron does accelerate for some time
but then it collides with something (a nucleus,
another electron, etc.).
• After the collision, the electron goes off in
some random direction, giving it momentarily
a zero average velocity.
• The drift velocity is the average velocity in the
a F qE
v



time between collisions:
2 2m 2m
d
Which of the following statements is false?
1) An electric field is needed to produce an electric
current.
2) A potential difference between two points is
needed to produce an electric current.
3) For a steady current to flow in a wire, the wire
must be part of a closed circuit.
4) The electric field is constant along all parts of the
circuit when a steady current is flowing.
5) The electric current in a wire is proportional to the
drift velocity of the charges.
Ohm’s Law
• Current through a resistor (ohmic device) is
proportional to the potential difference across
it.
V  IR
vd 
qE
2m
I  qnAvd
q 2 nAE
I
2m
q 2 nA V
I
2m l
Resistance and Resistivity
• Resistance depends on the geometry of the
resistor – its length and cross-sectional area
– R is proportional to length
– R is inversely proportional to area.
rl
R
A
• Resistivity r depends on material properties
like how often charges scatter.
Wire A, which is of the same length and
material as wire B, has twice the diameter of
wire B. If the resistance of wire B is R, what
is the resistance of wire A?
1) R
2) 2R
3) R/2
4) 4R
5) R/4
Emf
• Emf (Electromotive “force”) – the voltage
provided by some voltage source (e.g. a
battery).
• A source of emf converts non-electrical energy
to electrical energy.
• E.g. electrical generator (turns mechanical energy
into electrical)
Which of the relations
among the quantities in the
figure is generally correct?
1)
I1R1 = I2R2
2)
I3R3 = I4R4
3)
I1R1 = I4R4
4)
I3R4 = I4R3
5)
I1R1 + I2R2 = e
Power in a circuit
E
P
t
• Power:
• In time t, a charge Q enters on the left and
Q exits on the right.
Vb
Va