What is the relationship between conductance and conductivity? Is there any formula that can explain their relationship?
[Physics] Conductance and conductivity
conductorselectric-circuitselectrical-resistance
Related Solutions
This DTIC Report (PDF) shows that the conductivity of silicon continues to increase as temperatures increase from 500K to close to silicon's melting point at 1,687K:
This is due to the rapid increase in the number of free electrons and holes with increasing temperature.
As temperatures increase, phonon scattering increases and this reduces the mobility. The rate of increase of scattering with temperature is much less than the rate of increase in free electrons and holes with temperature. Hence, conductivity continues to increase as temperature rises.
Intrinsic vs extrinsic
The plot below, from the same report, shows how the conductivity of intrinsic silicon (samples 5 & 6) compare with doped (extrinsic) silicon (samples 1 and 2). Note that, unlike the plot above, the scale of the top axis on the plot below is in centigrade, not Kelvin:
At low temperatures, the doped silicon has higher conductivity than the intrinsic silicon semiconductor. As temperature increases, the conductivity of the doped Si drops slightly to due increased scattering. As temperatures increase further, the growth in thermal carriers becomes more important than the increase in scattering. As temperature increases further, the conductivity also increases.
$R$ is given by: $$ R = \rho \frac{d}{A} $$ and $C$ by: $$ C = \epsilon \frac{A}{d} $$
Multiplying $R$ and $C$ gives us: $$ RC = \rho \epsilon $$
Capacitance and resistivity are unrelated, like Chemomechanics pointed out.
Best Answer
Conductance is the extrinsic property while conductivity is the intrinsic property. This means that conductance is the property of an object dependent of its amount/mass or physical shape and size, while conductivity is the inherent property of the material that makes up the object. No matter how the object changes in terms of shape/size/mass, as long as it is made of the same material and the temperature remains the same, its conductivity does not change. Conversely, the conductance of a conductor changes with its cross-sectional area and length. Of course, a higher conductivity also gives an object a higher conductance. The formula that relates conductivity with conductance is:
$$G=\sigma \frac A l$$
where $G$ is the conductance, $σ$ the conductivity, $A$ the cross-sectional area perpendicular to the direction of electric current, and $l$ the length of the conductor. This formula applies for any (geometrically) prismic or cylindrical conductor, including cuboids.