Final answer:
The value of the resistance in the circuit is calculated using the power formula P = I^2R. Given the power is 100 W and the current is 3 A, the resistance is 11.11 Ohms.
Step-by-step explanation:
The question asks us to calculate the value of the resistance in a circuit where heat energy is produced at a rate of 100 W, and the current flowing through the circuit is 3 A.
The power (P) dissipated as heat in a resistor can be calculated using the formula P = I2R, where I is the current and R is the resistance. Solving for R gives us R = P / I2. Substituting the given values, we have R = 100 W / (3 A)2 = 100 W / 9 A2 = 11.11 Ohms. Therefore, the resistance must be 11.11 Ohms.