If the electric current flowing through an ohmic heating element is increased by 50 percent (I' = 1.5 I) while maintaining constant resistance, by what percentage does the rate of heat dissipation (electric power) increase?
Answer and explanation
Correct answer: D. 125 percent increase
- Step 1: According to Joule's heating law, electric power dissipation at constant resistance is: .
- Step 2: When current increases by 50%, the new current is: .
- Step 3: The new power dissipation is: .
- Step 4: The fractional increase in power is: .
- Step 5: Convert to percentage: .
Answer
125 percent increase
Why not the others: '50 percent increase' incorrectly assumes power is directly proportional to current ( instead of ); '100 percent increase' is arbitrary; '225 percent increase' confuses the final percentage of initial power () with the net increase ().
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