Question

As the temperature of a conductor increases, its resistivity and conductivity change. The ratio of resistivity to conductivity _______________ .

Options

• increases

• decreases

• remains constant

• may increase or decrease, depending on the actual temperature

Answer 1

increases

 

Resistivity (ρ) of a conductor is the reciprocal of the its conductivity(σ). Thus,

\[\rho = \frac{1}{\sigma}\]

The ratio of the resistivity and the conductivity,

\[\frac{\rho}{\sigma} = \frac{\rho}{1/\rho} = \rho^2\]

As resistivity increases with temperature, the square of resistivity will also increase. Hence, the ratio of resistivity and conductivity will increase with increase in temperature.