According to Joule's law of heating, the rate of heat produced in a r…

The correct answer is Option (4) → (B), (C) and (D) only

By Joule's law the rate of heat production in a resistor is the power dissipated, \( P = I^{2}R = V^{2}/R \).

(A) directly proportional to the current for the given resistance — Incorrect. For a given \( R \), \( P = I^{2}R \) varies as the square of the current, not as the current.

(B) directly proportional to the square of the current for the given resistance — Correct. \( P = I^{2}R \propto I^{2} \) when \( R \) is fixed.

(C) directly proportional to the resistance for a given value of current — Correct. \( P = I^{2}R \propto R \) when \( I \) is fixed.

(D) inversely proportional to the resistance for a given voltage — Correct. \( P = V^{2}/R \propto 1/R \) when \( V \) is fixed.

Statements (B), (C) and (D) are correct, which is Option (4).

NCERT (2026-27):
Electrical Energy, Power – “… The energy dissipated per unit time is the power dissipated P = ΔW/Δt and we have,

    \( \displaystyle P = IV \qquad (3.32) \)

Using Ohm’s law V = IR, we get

    \( \displaystyle P = I^2 R = V^2/R \qquad (3.33) \)

as the power loss (“ohmic loss”) in a conductor of resistance R carrying a current I. It is this power which heats up, for example, the coil of an electric bulb to incandescence, radiating out heat and light.”