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## 2/1/15

### Electric Resistance.

Resistance.

The electric resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor.

Depending on Voltage (a measure of how much force the electrons are under) & Resistance, the electric current (Amperage, amount of electrons moving in a circuit) can be deteremined as stated by Ohm's law.

Unit of Resistance is Ohm (Ω); [R] = Ω.

For example:

We can say that value of Resistance is 200 Ω.

R = 200 Ω.

Conductance.

The inverse quantity of Resistance is electric conductance, the ease with which an electric current passes.

Unit of conductance is siemens (S); [G] = S.

For example:

We can say that value of Conductance is 5 mS.

1/R = G = 5 mS = 1/200 Ω.

Resistivity.

Resistance of a conduct wire depends on:
- length,
- gauge,
- material type.

Resistivity ρ of a conduct wire is a resistance of a conduct wire with length of 1 m, gauge of 1 mm2, measured in a temperature of 20o C.

Unit of Resistivity ρ of a conductor is Ω mm2/m.

Conductivity.

Conductivity γ is inverse value of conduct wire's resistivity ρ.

Physical equations related.

R = 1 / G.

where:
- R: Resistance,
- G: Conductance.

R = (ρ · l) / S = l / (γ · S).

where:
- R: Resistance,
- ρ: Wire's resistivity,
- l: Wire's length,
- S: Wire's gauge,
- γ: Wire's conductivity.

Ohm's law.

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points.

Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

I = U / R,

where:
- I: the current through the conductor in units of amperes,
- U: the potential difference measured across the conductor in units of volts,
- R: the resistance of the conductor in units of ohms.

More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

U / I = R = const.

Resistance & Temperature.

Resistance of conducting materials depends on temperature.

Carbon, as well as most semiconductors conducts electric current better in hot state than in cold state. These materials are called conductors with resistance's negative temperature coefficient (NTC). Resistance lowers with increase in temperature.

Other semiconductors, conduct electric current better in cold state than in hot state. These materials are called conductors with resistance's positive temperature coefficient (PTC). Resistance increases with increase in temperature.

Magnitude of resistance change is described by temperature coefficient of resistance α.

Temperature coefficient of resistance α shows by how many ohms (Ω) resistance changes with temperature change of 1 (K).

ΔR = α · R1 · Δθ.
Δθ = θ2 - θ1.
R2 = R1 + ΔR.
R2 = R1(1 + α · Δθ).

where:
- ΔR: resistances difference,
- α: temperature coefficient,
- R1: resistance in temperature θ1,
- R2: resistance in temperature θ2,
- Δθ: temperatures difference,
- θ1: temperature at beginning,
- θ2: temperature at end.

Sources: Wikipedia on Resistance & Conductance, Wikipedia on Ohm's law, Wikpedia on Temperature Coefficient, [41].