Current, Ohm’s Law, Etc. where R is resistance Resistance does not vary with the applied voltage...
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Transcript of Current, Ohm’s Law, Etc. where R is resistance Resistance does not vary with the applied voltage...
Current, Ohm’s Law, Etc.
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V where R is resistance
Resistance does not vary with the applied voltage
resistor
Ampere
VoltsR
Experimentally it is found that R depends on the material the wire is made of and its dimensions. Does not depend on the shape.
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In a wire of uniform resistivity and cross sectional area, the electric field is a constant for constant currents.
+
-V i
l
VA
l
VA
R
Vi
1
i
Exercise 1810
Given the resistivity of copper, about Ohm-m, what length of 0.5 cm diameter wire will yield a resistance of 10 Ohms?
Current Density
S
Sdji
Consider current flowing in a homogeneous wire with cross sectional area A.
jAdSjjdSSdjiA A A
A
ij
The Continuity Equation for Steady State Currents
0Sdj
Currents and current densities are constant in time – steady state. The flux of out of any closed surface must be zero.
j
Another form of Ohm’s Law
Ej
jE
For steady state situation
0 Sdj
0 rdE
Metal: ρ increases with increasing T
T
Resistivity and temperature
Semiconductors: ρ decreases with increasing T
T
Superconductor
T
0
cTTfor 0
cT
Once a current has been established in a superconducting ring, it continues indefinitely without the presence of any driving field.
1911 Dutch physicist Heike Kamerlingh Onnes - HgKTc 2.4
2003 KTc 160
Water Nitrogen Oxygen
Boils
Freezes
100 C (212 F) -196 C (-322 F) -183 C (-297 F)
0 C (32 F) -210 C (-346 F) -223 C (-369 F)
Our air is ¾ Nitrogen and ¼ Oxygen
• 1908- liquefied helium produced
• First discovered in mercury by Kamerlingh-Onnes in 1911.
• Critical temperature 4.21K.
• Nobel Prize in 1913.
Superconductivity
High-Tc Superconductivity
Liquid nitrogen temperature 77 K
Complex ceramic materials were discovered in 1986. They exhibit superconductivity at much higher temperatures – above LN temperature!
Muller and Bednortz, Nobel Prize 1987
Meissner effect and magnetic levitation
