Question

Which uses more energy, a 250W TV set in 1 hr, or a 1200W toaster in 10 minutes?

Answer 1

Hint: Power of a device can be defined as the rate at which that device does work. It is equal to the time rate of doing work. By calculating work done by two devices we can compare how much energy they are using.

Formula used:
Power of device is the rate of doing work given as
$P = \dfrac{W}{t}$
where P is the power of the device, W represents the amount of work that the device is doing, t represents the duration of time for which the device does work.

Detailed step by step solution:
We are given the power rating of a TV set and a toaster.
First, consider the TV set. It has power given as
${P_1} = 250W$
The duration for which it is operated is given as
${t_1} = 1h = 3600s$
Now, the work done by the TV set is equal to the product of its power and time for which it is operated. Therefore, we can write
${W_1} = {P_1} \times {t_1} \\\ = 250 \times 3600 \\\ = 9 \times {10^5}J \\\$
This is the energy used by the TV set in 1hr duration.
Next, we have a toaster. It has power given as
${P_2} = 1200W$
The duration for which it is being operated is given as
${t_2} = 10\min = 10 \times 60s = 600s$
Now, the work done by the toaster is equal to the product of its power and time for which it is being operated. Therefore, we can write
${W_2} = {P_2} \times {t_2} \\\ = 1200 \times 600 \\\ = 7.2 \times {10^5}J \\\$
This is the energy used by the TOASTER in 10 min duration.
Therefore, we can say that a TV set uses more energy than the toaster.

Note: 1. The student must convert the units of time into seconds before solving the problem.
2. We notice that though the toaster had more power, its duration of operation was short due to which total energy spent was lesser compared to the TV set. Hence, it depends on time whether a device will use more or less energy.