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Q10
(NDA-I/2008)
Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism
Answer Verified
If the current is flowing through a 10 ohm resistor, then in which one of the following cases maximum heat will be generated?
Result
Your answer:
—
·
Correct:
C
Explanation
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.
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