The voltage V and current I graphs for a conductor at two different temperatures T₁ and T₂ are shown in the figure. The relation between T₁ and T₂ is ________

CONCEPT:

• Ohm's Law: It is a law that states that electric current is proportional to voltage and inversely proportional to resistance. Mathematically,

V = IR

where R is the resistance, I is current, and V is the voltage across the conductor.

\(R = {V \over I}\)

• The slope of the V-I graph gives the resistance of a conductor at a given temperature.​​​

• Conductor: The material that allows the electric current to flow through them is called the conductor.
  • The resistance of a conductor increases by increasing the temperature.

The relation between resistance of a conductor and temperature is given by:

\({R_t} = {R_o}\left[ {1 + α \left( {T - {T_o}} \right)} \right]\)

Where Rt = resistance at temperature t°, Ro = resistance at temperature 0°, and α = temperature co-efficient of resistance.

• ​Higher the slope, the higher the resistance, the higher the temperature, and vice-versa.
• The resistance of a conductor increases with an increase in temperature for conductors and vice versa.

EXPLANATION:

• From the graph, it can be said that the slope of the graph at T₁ is greater than the slope of the graph at T₂
• ​Higher the slope, the higher the resistance, the higher the temperature, and vice-versa.
• So, it can be said that the resistance of a conductor at temperature T₁​ is greater than at temperature T₂ i.e.

\(T_1>T_2\)

• So the correct answer is option 1.