Current, Resistance, and
Electromotive Force
Sections 1-5, 7
Chapter 28
1
Current



Movement of charges
Scalar quantity
Amount of charge transferred per unit time
Q
I
t


2
Measured in amperes or amps
1A = 1 C/s
Traditional current direction



3
Current flows in the direction that positive
charge would flow.
It is impossible to experimentally determine
which charges are moving.
We know that the electrons are actually
moving in the opposite direction of current
flow, but we keep with tradition.
Drift velocity




4
Speed of the moving particles.
n particles per unit volume are moving in a
conductor with speed v.
In a time t, each particle moves vt.
If the conductor has a cross sectional area A,
then the number of particles in a given
section during a given time interval is nAvt.
Drift velocity

If each particle has a charge q, the total
charge moving through the volume in a given
time interval is Q = nqvAt.
Q
I
 nqvA
t
5
Current density

Current per unit cross-sectional area
I
J   nqv
A
6
Resistivity

Ratio of electric field to current density
E

J


7
Big resistivity means that a big E field is
needed to cause a given current density,
Or that a small E field will cause a small
current density
Resistivity

For metals, increases with temperature.
T  0 1   T  T0 


8
For semiconductors, it decreases with
temperature.
For superconductors it drops suddenly as
temperature decreases.
Resistance




Related to resistivity.
Often more useful, because it uses total
current, not current density. It also uses
potential difference instead of E field.
Measured in ohms
1 W = 1 V/A
R
9
l
A
Ohm’s Law

Very important
V  IR
10
Temperature dependence
RT  R0 1   T  T0 
11
Resistors


12
Circuit elements designed to have a specific
resistance.
Used to control current.
Circuits



13
We need a complete circuit to have a steady
current.
Charge moves in the direction of decreasing
potential energy – like rolling downhill.
We need to have a device to move the
charge back uphill – like the pump in a
fountain.
Electromotive force





14
What makes the charge move from lower to
higher potential.
Abbreviated emf – say each letter.
Batteries
Solar cells
Generators
Circuits



15
Contain resistors, sources of emf, and
possibly other circuit elements.
The algebraic sum of the potential
differences around the path is zero.
In a simple loop, the current is the same
everywhere.
Sources of emf


Maintain a constant potential difference, or
voltage, regardless of the current flowing
through them.
Have positive and negative terminals.
–
The potential is higher at the positive terminal.
E V
16
Internal resistance


Real sources of emf have some internal
resistance to current flow.
So,
V  E  Ir
E  Ir  IR
E
I
Rr
17
Example on page 632

18
Look at schematic drawings of circuits.
Kirchoff’s loop rule


The sum of the voltages around a loop is
zero.
Choose a current direction and draw it on the
diagram. It’s OK if you’re wrong.
–
19
If at the end we get negative current, then the
direction was wrong. No big deal.
Kirchoff’s loop rule



20
If we go across a battery from – to +, we add
the voltage. + to – we subtract it.
Always subtract IR from a resistor
See example on page 635
Power





Work done per unit time, measured in watts.
1 W is 1 J/s
1 A is 1 C/s
1 V is 1 J/C
(1A)(1V) = 1 J/s
P  IV
21
Power

Using Ohm’s law, V = IR
P  I IR 
PI R
2
22
V 
P   V
R
2
V
P
R
Power output of emf source
P  IV  IE  I r
2
23
Power input of emf source
P  IV  IE  I r
2
24
Physiological effects of currents



25
Nervous system is electrical
Currents as low as 1 mA can disrupt the
nervous system enough to cause death by
fibrillation.
Larger currents through the heart may
actually be safer – the heart is temporarily
paralyzed and has a better chance of
restarting with a normal heartbeat