A potential difference of 12V is applied across the ends of a 6$\Omega$ resistor for 10 minutes. Determine the quantity of heat generated

Analyze the question A resistor connected to a potential difference for a certain time produces heat. We need the heat energy generated.

Concept Electrical energy converted to heat is given by:

H = V²t / R

(or H = I²Rt = VIt, which are all equivalent.)

Important: time must be in seconds.

Solution

Given:

• V = 12 V
• R = 6 Ω
• t = 10 minutes = 10 × 60 = 600 s

Step 1: Find the current I = V/R = 12/6 = 2 A

Step 2: Find the heat H = I²Rt = (2)² × 6 × 600 H = 4 × 6 × 600 H = 24 × 600 = 14,400 J

Check with the other formula: H = V²t/R = (144 × 600)/6 = 144 × 100 = 14,400 J ✔

Answer: The heat generated is 14,400 J, which is option C.

Tip The common mistake is forgetting to convert minutes to seconds. If you used 10 directly, you'd get 240 J, which isn't an option. Always convert time to seconds first. Also, if you see V and R given, jump straight to H = V²t/R to save time.