The resistance of a bagel toaster is 15 Ω. To prepare a bagel, the toaster is operated for one minute from a 120-V outlet. How much energy is delivered to the toaster?
P = V^2/R = 120^2/15 = 960 Watts.
Energy = P * t = 960 * 60s = 57,600 Watt-seconds.
To calculate the energy delivered to the toaster, we can use the formula:
Energy (E) = Power (P) × Time (t)
First, let's calculate the power used by the toaster using Ohm's Law:
Power (P) = (Voltage (V))² / Resistance (R)
Given that the resistance of the toaster is 15 Ω and the voltage from the outlet is 120 V, we can plug these values into the formula:
Power (P) = (120 V)² / 15 Ω
Calculating this, we get:
Power (P) = 9600 W / 15 Ω
Power (P) = 640 W
Now that we have the power used by the toaster, we need to calculate the time it was operated. In the question, it states that the toaster was operated for one minute, so we can substitute this value into the formula:
Time (t) = 1 minute
Now we can calculate the energy delivered to the toaster:
Energy (E) = Power (P) × Time (t)
Energy (E) = 640 W × 1 minute
Since energy is typically measured in joules (J) or watt-hours (Wh), we can convert the energy from watts and minutes to joules or watt-hours.
To convert watt-minutes to joules, we multiply by 60 since there are 60 seconds in a minute:
Energy (E) = (640 W × 1 minute) × 60 s/min
Energy (E) = 38,400 J
To convert watt-minutes to watt-hours, we divide by 60 since there are 60 minutes in an hour:
Energy (E) = (640 W × 1 minute) / 60 min/h
Energy (E) = 10.67 Wh
Thus, the energy delivered to the toaster is either 38,400 joules (J) or 10.67 watt-hours (Wh), depending on the desired unit.