A 12$\Omega$ resistor dissipates 8kJ of heat in 20s. Calculate the current through the resistor

Analyze the question: A resistor of 12 Ω dissipates 8 kJ of heat in 20 s. We need the current through it.

Concept: Electrical energy dissipated as heat is H = I²Rt so I = √(H / Rt)

Solution:

• H = 8 kJ = 8000 J
• R = 12 Ω
• t = 20 s

I² = H / (R × t) = 8000 / (12 × 20) = 8000 / 240 = 33.33

I = √33.33 ≈ 5.77 A ≈ 5.8 A

Answer: The current is about 5.8 A, which matches option A.

Check on the other options: 33.3 (option D) is I², not I. Students who forget to take the square root fall into this trap. Option C (30 A) and option B (6.9 A) don't come from the correct formula.

Tip: When the question gives energy, resistance and time, use H = I²Rt. Always take the square root at the end, because the value you compute first is I², not I. Also remember to convert kJ to J (multiply by 1000).