Which of the following statements best describe the temperature dependence of resistances of Cu and Si in the temperature range 27° to 127°C.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Linear increase for Cu and exponential decrease for Si
Copper is a metal and silicon is a semiconductor, and their resistances change with temperature in opposite ways.
Copper. A rise in temperature makes the ions vibrate more, so the electrons collide more often and the relaxation time falls. Over a limited range of temperature the resistance rises almost linearly:
\( R_T = R_0\left[1 + \alpha(T - T_0)\right] \)
Silicon. A rise in temperature frees many more charge carriers (electrons and holes), and this effect is much stronger than the fall in their mobility. The number of carriers grows exponentially with temperature, so the resistance decreases exponentially.
NCERT (2026-27):
Temperature Dependence of Resistivity – “… Over a limited range of temperatures, that is not too large, the resistivity of a metallic conductor is approximately given by,
\( \displaystyle \rho_T = \rho_0\left[1 + \alpha\left(T - T_0\right)\right] \qquad (3.26) \)
… For metals, α is positive. The relation of Eq. (3.26) implies that a graph of ρT plotted against T would be a straight line.”
Temperature Dependence of Resistivity – “… Unlike metals, the resistivities of semiconductors decrease with increasing temperatures. A typical dependence is shown in Fig. 3.10.”