Is it true or false that the total amount of heat produced in a conductor is inversely proportional to resistance times the square of the current?

Is it true or false that the total amount of heat produced in a conductor is inversely proportional to resistance times the square of the current?

• A. True
• B. False
• C. Partly true
• D. Not applicable

Answer: (B)

The relationship between heat produced in a conductor, resistance, and current is defined by the formula \( P = I^2 R \), where \( P \) is the power (heat) produced, \( I \) is the current, and \( R \) is the resistance. According to this formula, the heat generated in a conductor is directly proportional to the square of the current and directly proportional to the resistance. Therefore, if current increases, the heat increases as the square of that current and if resistance increases, it also increases the heat produced. The notion of "inversely proportional" indicates that as one quantity increases, the other decreases, which does not apply in this scenario. Instead, both resistance and the square of the current contribute positively to the total heat produced. Thus, the statement that the total amount of heat produced is inversely proportional to resistance times the square of the current is false.

The relationship between heat produced in a conductor, resistance, and current is defined by the formula ( P = I^2 R ), where ( P ) is the power (heat) produced, ( I ) is the current, and ( R ) is the resistance. According to this formula, the heat generated in a conductor is directly proportional to the square of the current and directly proportional to the resistance. Therefore, if current increases, the heat increases as the square of that current and if resistance increases, it also increases the heat produced.

The notion of "inversely proportional" indicates that as one quantity increases, the other decreases, which does not apply in this scenario. Instead, both resistance and the square of the current contribute positively to the total heat produced. Thus, the statement that the total amount of heat produced is inversely proportional to resistance times the square of the current is false.