An electric heater has a resistance of 50 . When it is immersed in water and connected to mains source, it…

Analyze the question: A heater of resistance R = 50 Ω carries a current I = 4.0 A for t = 2 minutes. With no heat losses, all the electrical energy becomes heat in the water.

Concept: Electrical energy converted to heat is given by Joule's law:

H = I²Rt

(Equivalent forms are H = VIt and H = V²t/R.)

Solution:

1. Convert time to seconds: t = 2 × 60 = 120 s
2. Substitute the values: H = (4.0)² × 50 × 120
3. Calculate step by step: • (4.0)² = 16 • 16 × 50 = 800 W (this is the power) • 800 × 120 = 96,000 J

Check using V = IR: V = 4 × 50 = 200 V, so H = VIt = 200 × 4 × 120 = 96,000 J. ✔

Answer: The heat gained by the water is 96,000 J, which is option D.

Tip: Always convert minutes to seconds before using energy formulas. A common mistake is to use t = 2 directly, which gives 1,600 J (option B), a distractor. When you have I and R, use H = I²Rt. When you have V and R, use H = V²t/R.