To determine the power loss in the cables of an electric generator, we can use the formula for power loss due to resistance in electrical circuits. The power loss (P_loss) in a resistor can be calculated using the formula: \[ P_{\text{loss}} = I^2 R \] where: - \( P_{\text{loss}} \) is the power loss in watts (W), - \( I \) is the current in amperes (A), - \( R \) is the resistance in ohms (Ω). ### Step 1: Calculate the Current (I) First, we need to find the current flowing through the cables. We can use the power output of the generator and the voltage to find the current using the formula: \[ P = V \times I \] Rearranging this formula to solve for current gives us: \[ I = \frac{P}{V} \] Given: - Power output \( P = 3.0 \, \text{KW} = 3000 \, \text{W} \) - Voltage \( V = 1.5 \, \text{KV} = 1500 \, \text{V} \) Now, substituting the values into the formula: \[ I = \frac{3000 \, \text{W}}{1500 \, \text{V}} = 2.0 \, \text{A} \] ### Step 2: Calculate the Power Loss (P_loss) Now that we have the current, we can calculate the power loss in the cables using the resistance given: - Resistance \( R = 20.0 \, \Omega \) Substituting the values into the power loss formula: \[ P_{\text{loss}} = I^2 R = (2.0 \, \text{A})^2 \times 20.0 \, \Omega \] Calculating \( I^2 \): \[ (2.0 \, \text{A})^2 = 4.0 \, \text{A}^2 \] Now substituting this back into the power loss equation: \[ P_{\text{loss}} = 4.0 \, \text{A}^2 \times 20.0 \, \Omega = 80.0 \, \text{W} \] ### Conclusion The power loss in the cables is **80.0 W**. Therefore, the correct option is: **A. 80.0 W** ### Explanation of Other Options - **B. 40.0 W**: This option is incorrect because it does not account for the correct calculation of current and resistance. If the current were lower, it would yield a lower power loss, but our calculations show that the current is 2.0 A. - **C. 10.0 W**: This option is also incorrect. It suggests an even lower power loss, which would imply either a much lower current or resistance, neither of which is true in this scenario. - **D. 0.1 W**: This option is significantly lower than the calculated power loss. Such a low power loss would only occur with very low current or resistance, which is not the case here. ### Revision Summary - Power loss in a resistor is calculated using \( P_{\text{loss}} = I^2 R \). - Current can be found using \( I = \frac{P}{V} \). - For this problem, the current was calculated to be 2.0 A, leading to a power loss of 80.0 W. - Always ensure to convert units properly (e.g., kW to W, kV to V) before performing calculations.