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A 33 Ω half-watt resistor and a 330 Ω half-watt resistor are connected across a 12 V source. Which one(s) will overheat?
Answer & Solution
Correct Answer:
Option
D
To determine which resistor will overheat, we need to calculate the power dissipated in each resistor and compare it with their power rating (0.5 watts).
Using the power formula: P = V² / R
For the 33 Ω resistor:
P = (12)² / 33 = 144 / 33 ≈ 4.36 watts
This is much greater than 0.5 watts, so the 33 Ω resistor will overheat.
For the 330 Ω resistor:
P = (12)² / 330 = 144 / 330 ≈ 0.436 watts
This is less than 0.5 watts, so the 330 Ω resistor will NOT overheat.
Conclusion: Only the 33 Ω resistor will overheat.
Using the power formula: P = V² / R
For the 33 Ω resistor:
P = (12)² / 33 = 144 / 33 ≈ 4.36 watts
This is much greater than 0.5 watts, so the 33 Ω resistor will overheat.
For the 330 Ω resistor:
P = (12)² / 330 = 144 / 330 ≈ 0.436 watts
This is less than 0.5 watts, so the 330 Ω resistor will NOT overheat.
Conclusion: Only the 33 Ω resistor will overheat.
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LoginTotal Resistance R(Tot)= 330 Ohm
Current flow through resistors (V/R Tot)= 0.036 Amp
Power dissipated through 33 ohm resistor (I2R) = 0.042 W less than 0.5 W
Power dissipated through 330 ohm resistor (I2R) = 0.43 W less than 0.5 W
So, neither resistors will heat......
"The rate at which heat is dissipated is called power" by formula : Power = heat/time.
So power is directly proportional to heat so if power rating is the same of each resistor so heat dissipation will also be the same. So neither of the resistor will be heated up at the power rating of 0.5 watts. (Across means Parallel)