The current-voltage graphs for a given metallic wire at two different temperatures, \( T_1 \) and \( T_2 \) are shown in the figure. The correct relation of temperatures and resistances will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( R_{T_2} \gt R_{T_1},\ T_2 \gt T_1 \)
On an \( I \)-\( V \) graph the slope is \( 1/R \). The line for \( T_1 \) is steeper than the line for \( T_2 \), so \( T_1 \) has the smaller resistance and \( T_2 \) the larger: \( R_{T_2} \gt R_{T_1} \).
For a metal, the resistance increases with temperature. The wire with the larger resistance is the hotter one, so \( T_2 \gt T_1 \).
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,
\( \displaystyle \rho_T = \rho_0 \left[1 + \alpha (T - T_0)\right] \qquad (3.26) \)
… For metals, α is positive.”