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Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, [1] one arrives at the three mathematical equations used to describe this relationship: [2]
The resistance of a given object depends primarily on two factors: what material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire.
The resistance of a given element is proportional to the length, but inversely proportional to the cross-sectional area. For example, if A = 1 m 2 , ℓ {\displaystyle \ell } = 1 m (forming a cube with perfectly conductive contacts on opposite faces), then the resistance of this element in ohms is numerically equal to the resistivity of the ...
Ohm's law states that the voltage across a resistor is proportional to the current passing through it, where the constant of proportionality is the resistance (). For example, if a 300- ohm resistor is attached across the terminals of a 12-volt battery, then a current of 12 / 300 = 0.04 amperes flows through that resistor.
Plot of the Wiedemann–Franz law for copper. Left axis: specific electric resistance ρ in 10 −10 Ω m, red line and specific thermal conductivity λ in W/(K m), green line. Right axis: ρ times λ in 100 U 2 /K, blue line and Lorenz number ρ λ / K in U 2 /K 2, pink line. Lorenz number is more or less constant.
An I–V curve which is a straight line through the origin with positive slope represents a linear or ohmic resistor, the most common type of resistance encountered in circuits. It obeys Ohm's law; the current is proportional to the applied voltage over a wide range. Its resistance, equal to the reciprocal of the slope of the line, is constant ...
The constant of proportionality is the thermal conductivity; it is a physical property of the material. In the present scenario, since T 2 > T 1 {\displaystyle T_{2}>T_{1}} heat flows in the minus x-direction and q {\displaystyle q} is negative, which in turn means that k > 0 {\displaystyle k>0} .
Resistance R is proportional to the distance l between the electrodes and is inversely proportional to the cross-sectional area of the sample A (noted S on the figure above). Writing ρ (rho) for the specific resistance, or resistivity, =.