A 1500-W baseboard heater runs on 240 mathrm(~V) . 16 a) What is the resistance of the baseboard heater? Answer: b) If the baseboard heater is on for an average of six hours per day, how much energy, in KWh, will it use in a week? Answer:

To solve the problem, let's break it into two parts:<br /><br />---<br /><br />### **Part (a): Resistance of the baseboard heater**<br /><br />We are given:<br />- Power (\(P\)) = 1500 W<br />- Voltage (\(V\)) = 240 V<br /><br />The formula for power in terms of resistance is:<br /><br />\[<br />P = \frac{V^2}{R}<br />\]<br /><br />Rearranging to solve for \(R\) (resistance):<br /><br />\[<br />R = \frac{V^2}{P}<br />\]<br /><br />Substitute the given values:<br /><br />\[<br />R = \frac{240^2}{1500}<br />\]<br /><br />\[<br />R = \frac{57600}{1500} = 38.4 \, \Omega<br />\]<br /><br />So, the resistance of the baseboard heater is:<br /><br />\[<br />\boxed{38.4 \, \Omega}<br />\]<br /><br />---<br /><br />### **Part (b): Energy usage in a week**<br /><br />We are given:<br />- Power (\(P\)) = 1500 W<br />- Time per day = 6 hours<br />- Number of days in a week = 7<br /><br />First, calculate the total time the heater is on in a week:<br /><br />\[<br />\text{Total time} = 6 \, \text{hours/day} \times 7 \, \text{days} = 42 \, \text{hours}<br />\]<br /><br />Next, calculate the energy used in kilowatt-hours (kWh). Recall that:<br /><br />\[<br />\text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (hours)}<br />\]<br /><br />Convert the power from watts to kilowatts:<br /><br />\[<br />\text{Power (kW)} = \frac{1500}{1000} = 1.5 \, \text{kW}<br />\]<br /><br />Now calculate the energy:<br /><br />\[<br />\text{Energy} = 1.5 \, \text{kW} \times 42 \, \text{hours} = 63 \, \text{kWh}<br />\]<br /><br />So, the energy used in a week is:<br /><br />\[<br />\boxed{63 \, \text{kWh}}<br />\]<br /><br />---<br /><br />### Final Answers:<br />(a) Resistance of the baseboard heater: \( \boxed{38.4 \, \Omega} \) <br />(b) Energy used in a week: \( \boxed{63 \, \text{kWh}} \)