Physics · Current Electricity · NEET
No. Conductance G = 1/R depends on the actual object (its length, area and material), so a long wire and a short wire of the same metal have different conductance. Conductivity sigma = 1/rho depends ONLY on the material, not on shape or size. They are linked by G = sigma*A/L, exactly like R = rho*L/A. In NEET, if the question gives a specific wire or resistor, it wants conductance; if it compares materials like silver, silicon and glass, it wants conductivity.
Conductance G has the unit siemens (S). Conductivity sigma has the unit siemens per metre (S/m or S m^-1). Check it with the formula: sigma = 1/rho, and rho has unit ohm-metre, so 1/(ohm-metre) = (1/ohm)/metre = S/m. Students often write both as 'siemens' and lose the mark. Conductance = S, conductivity = S/m.
Yes. 1 siemens = 1 ohm-inverse = 1 mho. 'Mho' is just 'ohm' spelt backwards and was the older name; the modern SI name is siemens (symbol S). So if an option says mho and another says siemens, they mean the same unit of conductance.
No. Conductivity sigma is a material constant at a fixed temperature, so cutting, stretching or bending copper does not change its conductivity. What changes is the conductance G of that piece, because G = sigma*A/L and cutting or stretching changes L and A. This is the classic trap: shape changes conductance, not conductivity.
From the microscopic form sigma = n*e^2*tau/m, conductivity depends on the number of free carriers per volume (n) and the relaxation time tau. In metals, heating lowers tau (more collisions) so sigma falls. In semiconductors, heating sharply raises n (more free carriers) so sigma rises. That is why metals conduct worse when hot but semiconductors conduct better when hot.
On the basis of electrical conductivity, which one of the following materials has the smallest resistivity?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
G = sigma*A/L, where A is cross-section area and L is length. This mirrors R = rho*L/A. Conductance is the inverse of resistance and conductivity is the inverse of resistivity.
Conductivity sigma has dimensions [M^-1 L^-3 T^3 A^2]. You can get it from sigma = 1/rho, since resistivity rho has dimensions [M L^3 T^-3 A^-2].
sigma = n*e^2*tau/m, where n is free-electron density, e is electron charge, tau is relaxation time and m is electron mass. This comes from combining drift velocity with Ohm's law J = sigma*E.
J = sigma*E, where J is current density and E is the electric field inside the conductor. This is the microscopic form of Ohm's law and is very useful in NEET conceptual questions.
Silver has the highest electrical conductivity of all metals, slightly higher than copper. That is why silver appears as the 'smallest resistivity' answer in NEET material-comparison questions.
