Physics Lab
NiKey_96
ohms_law_formatted.pptxCurrent and Resistance
Electric Current
Electric current is the rate of flow of charge through some region of space.
The SI unit of current is the ampere (A).
1 A = 1 C / s
The symbol for electric current is I.
Section 27.1
Average Electric Current
Charges are moving perpendicular to a surface of area A.
ΔQ is the amount of charge that passes through A in time Δt.
The average current:
Section 27.1
Instantaneous Electric Current
If the rate at which the charge flows varies with time, the instantaneous current, I, is defined as the differential limit of average current as Δt→0.
Section 27.1
Direction of Current
It is conventional to assign to the current the same direction as the flow of positive charges.
In an ordinary conductor, the direction of current flow is opposite the direction of the flow of electrons.
It is common to refer to any moving charge as a charge carrier.
Section 27.1
Charge Carrier Motion in a Conductor
The zigzag black lines represents the motion of a charge carrier in a conductor in the presence of an electric field.
The net motion of electrons is opposite the direction of the electric field.
Section 27.1
Current & Drift Speed
The total charge is:
ΔQ = (nAΔx)q
The current is
Iave = ΔQ/Δt = nqvdA
vd = = Δx/Δt is an average speed called the drift speed.
Section 27.1
Current Density
Current density is defined as the current per unit area.
J ≡ I / A = nqvd
J has SI units of A/m2
The current density is in the same direction as the flow of positive charges.
Section 27.2
Conductivity
For some materials, the current density is directly proportional to the electric field.
The constant of proportionality, σ, is called the conductivity of the conductor.
Section 27.2
Ohm’s Law
Ohm’s law states that for many materials, the ratio of the current density to the electric field is a constant σ that is independent of the electric field producing the current.
J = σ E
Section 27.2
Ohm’s Law
Materials that obey Ohm’s law are said to be ohmic. However, Not all materials follow Ohm’s law.
Materials that do not obey Ohm’s law are said to be nonohmic.
Section 27.2
Resistance
In a conductor, the voltage drop across the ends of the conductor is proportional to the current through the conductor.
The constant of proportionality is called the resistance of the conductor.
SI units of resistance are ohms (Ω).
1 Ω = 1 V / A
Section 27.2
Resistors
Most electric circuits use circuit elements called resistors to control the current in the various parts of the circuit.
Values of resistors are normally indicated by colored bands.
Section 27.2
Resistivity
The inverse of the conductivity is the resistivity:
ρ = 1 / σ
Resistivity has SI units of ohm-meters (Ω . m)
Resistance is also related to resistivity:
Section 27.2
Resistance & Resistivity
Every ohmic material has a characteristic resistivity that depends on the properties of the material and on temperature.
Resistivity is a property of substances.
The resistance of a material depends on its geometry and its resistivity.
Resistance is a property of an object.
Section 27.2
Ohmic and Nonohmic
An ohmic devices (a)
The slope is related to the resistance.
Section 27.2
Nonohmic devices are those whose resistance changes with voltage or current (b).
Resistivity & Temperature
The resistivity of a conductor varies approximately linearly with the temperature.
ρo is the resistivity at some reference temperature To (usually taken to be 20°C)
α is the temperature coefficient of resistivity
The temperature coefficient of resistivity can be expressed as:
Temperature Variation of Resistance
Since the resistance of a conductor is proportional to the resistivity, you can find the effect of temperature on resistance.
R = Ro[1 + α(T - To)]
Section 27.4
Electric Power
The power is given by the equation P = I ΔV
Alternative expressions can be found:
Units: I is in A, R is in Ω, ΔV is in V, and P is in W
Section 27.6
avg
Q
t
D
=
D
I
dQ
dt
º
I
VRI
R
ñ
A
=
l
[1()]ooρραTT
1
o
T
r
a
r
D
=
D
(
)
2
2
V
PVR
R
D
=D==
II
