Question

The figure shows the voltage (V) versus the current (I) graphs for a wire at two temperatures \( T_1 \) and \( T_2 \). One can conclude that:

• A. \( T_2 = 2T_1 \)
• B. \( T_1>T_2 \)
• C. \( T_1 = \frac{T_2}{3} \)
• D. \( T_1<T_2 \)

Hint:

In an I–V graph, a steeper slope means higher conductance (lower resistance). Since resistance increases with temperature, a steeper slope means a lower temperature.

Answer 1

The Correct Option is D

The figure shows two I–V graphs for a wire at temperatures \( T_1 \) and \( T_2 \). Since the graph represents current \( I \) versus voltage \( V \), the slope of the line indicates the conductance \( \left( \frac{I}{V} \right) \), which is inversely proportional to resistance: \[ \text{slope} = \frac{I}{V} = \frac{1}{R} \] From the graph, the slope at \( T_1 \) is greater than the slope at \( T_2 \), which implies: \[ \frac{1}{R_1}>\frac{1}{R_2} \Rightarrow R_1<R_2 \] For most metallic conductors, resistance increases with temperature. Hence: \[ R_1<R_2 \Rightarrow T_1<T_2 \]