If the current is flowing through a 10 ohm resistor, then in which one of the following cases maximum heat will be generated?

The correct answer is Option 3. According to Joule’s Law of Heating, the heat generated (H) in a resistor is given by the formula: H = I²Rt, where I is the current, R is the resistance, and t is the time.

Given the resistance (R) is constant at 10 ohms, we calculate the proportionality factor (I²t) for each case:

• Option 1: 5² × 2 = 25 × 2 = 50 units
• Option 2: 4² × 3 = 16 × 3 = 48 units
• Option 3: 3² × 6 = 9 × 6 = 54 units
• Option 4: 2² × 12 = 4 × 12 = 48 units

Since the value of I²t is highest for 3 A in 6 minutes, Option 3 results in the maximum heat generation. This demonstrates that heat increases quadratically with current and linearly with time; in this specific comparison, the longer duration in Option 3 compensates for the lower current compared to Options 1 and 2.