Correct Answer  Option 3 :
\(\frac{1}{{e}}\)
Concept:
Electrical Energy and Joules Heating
The heat generated by a resistive coil or device is given as
\(H = \frac{V^2}{R}t = I^2 Rt\)
H is energy, t is time, R is resistance, V is the potential difference.
If the conductor is purely resistive, then the whole electrical energy is converted into heat energy.
Resistivity and Resistance
 The property of a conductor that opposes the flow of electric current through them and is independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.

Resistance: The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.
 It is denoted by R and the SI unit is the ohm (Ω).
 The resistance is given by:
\(⇒ R=\frac{ρ l}{A}\)
Calculation:
Given,
Potential difference V is constant
Resistance is proportional to resistivity e.
Given
\(H = \frac{V^2}{R}t \)
\(\implies H \propto \frac{1}{{R}}\)
R is proportional to e
\(\implies H \propto \frac{1}{{e}}\)
 The unit for resistivity is the ohmmeter (Ωm).
 The resistivity of a material depends on its nature and the temperature of the conductor.
 The resistivity of a material doesn't depend on its shape and size (length and area).