Download Resistance Resistivity and Conductivity

Resistance
How much “push” (electric potential) is needed to achieve a certain flow (electric
current)?
R=
V V

=
Ω
Ohm
=

i  A
A circuit element for resistor is indicated with the symbol:
Resistivity and Conductivity
Resistance is a property of a specific object, and so depends on the
geometry of that object. Resistivity is a property of a particular
material:
ρ=
E
J
[Ωm]
σ=
1
Ω −1m -1 
ρ
G
G
J =σE
G
G
E = ρJ
For simple geometry:
R=ρ
L
A
1
Temperature variations.
ρ − ρ 0 = ρ0α (T − T0 )
Ohm’s Law
Ohm’s Law: when the current through a device is proportional to the
voltage applied across the device.
When the resistance of the device is independent of the voltage across
it.
A material obeys Ohm’s law when the resistivity of the material is
independent of the applied magnetic field.
2
Power in Circuits
Remember that :
Power is the amount of energy transferred per time:
The amount of energy transferred to a charge q
traversing a potential difference:
SO:
P=
dE dqV
=
= iV
dt
dt
dE
dt
U = qV
P=
P = i2 R
For resistive circuits
(resistors):
V2
P=
R
Electromotive Force: Emf
What really happens in a battery?
Charge is “pumped” from a low potential to a higher potential, which
requires work. We define the EMF as the amount of work per amount
of charge:
E =
But note:
E =
∆W dW
=
∆q
dq
dW dqV
=
=V
dq
dq
The correct way to interpret this last equation is: The EMF
device causes a potential difference of V=E across it’s
terminals.
3
Single Current Loop
For the most simple circuits:
I
E
+
R
E
V
I= =
R R
4