Select the best answer for the question. A circuit with resistance of 25 ohms is carrying a current of 2. How much heat, in watts, is developed?
A. 450
B. 1250
C. 50
D. 100
Answer (2)
Identify the formula for power: P = I 2 × R .
Substitute the given values: I = 2 amperes and R = 25 ohms.
Calculate the power: P = ( 2 ) 2 × 25 = 100 watts.
State the final answer: The heat developed is 100 watts.
Explanation
Problem Analysis We are given a circuit with a resistance of 25 ohms and a current of 2 amperes. We need to find the heat developed in watts.
Formula Introduction The formula to calculate power (heat developed in watts) in a circuit is given by: P = I 2 × R where:
P is the power in watts,
I is the current in amperes,
R is the resistance in ohms.
Calculation We are given I = 2 amperes and R = 25 ohms. Substituting these values into the formula, we get: P = ( 2 ) 2 × 25 P = 4 × 25 P = 100
Conclusion Therefore, the heat developed in the circuit is 100 watts.
Examples
Understanding how to calculate heat dissipation in electrical circuits is crucial for designing safe and efficient electronic devices. For instance, when designing a smartphone, engineers need to calculate the heat generated by the processor to ensure it doesn't overheat. By knowing the resistance and current flow, they can use the formula P = I 2 × R to determine the power dissipated as heat, allowing them to implement appropriate cooling solutions and prevent damage to the device. This principle extends to various applications, from household appliances to industrial machinery, ensuring reliable and safe operation.
The heat developed in the circuit is 100 watts, calculated using the formula P = I 2 × R . Therefore, the correct answer is option D. 100.
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