Which uses more energy, a \(250 \mathrm{~W}\) TV set in \(1 \mathrm{hr}\), or a \(1200 \mathrm{~W}\) toaster in 10 minutes?

To understand the problem of comparing energy consumption, we first need to grasp the concepts of power and energy.
Power, denoted by the symbol \( P \), is the rate at which energy is used or transferred. It is measured in watts (W).
One watt is equivalent to one joule per second. In simple terms, power is how fast energy is being used.
Energy, represented as \( E \), is the capacity to do work. It can be thought of as the total amount of work done or heat generated.
The relationship between power and energy can be described with the formula:
\[ E = P \times t \] where \( P \) is power and \( t \) is time. This formula tells us that the energy consumed by an electrical device is the product of its power rating and the time it operates.
For example, a TV with a power rating of 250 watts running for 1 hour consumes an energy of 250 watt-hours (Wh).
This relationship will help us understand how to calculate and compare the energy usage of different appliances.

When discussing electrical appliances, you often encounter the terms watts (W) and watt-hours (Wh).
Watts measure the power, which is the rate at which an appliance uses energy.
Watt-hours, on the other hand, measure the total energy consumed over a period.
Think of it this way: watts tell you how fast energy is being consumed at any given moment, while watt-hours tell you the total amount of energy consumed over a period.
To illustrate, let's revisit our example: A 250-watt TV running for 1 hour consumes 250 watt-hours of energy. Here, watts (W) are used to indicate the power of the TV, and watt-hours (Wh) indicate the total energy consumed.
Similarly, a 1200-watt toaster running for 10 minutes (which is 1/6 of an hour) consumes 1200 watts \( \times \) 1/6 hours, which is 200 watt-hours.
By converting both values to watt-hours, we can easily compare them and see that the TV consumes more energy than the toaster within their respective usage times.

Accurately comparing energy consumption requires converting time into the same units. This ensures consistent comparisons.
In our examples, we had two different times: 1 hour for the TV and 10 minutes for the toaster.
To compare them, we converted the 10 minutes into hours, since we want to calculate energy in watt-hours.
10 minutes is the same as 10/60 hours or 1/6 hours. This conversion is crucial because the formula \( E = P \times t \) uses time in hours.
Without properly converting the time, we would not be able to accurately compare the energy values.
By converting the time for the toaster to hours, we made sure that we used the same unit of time when calculating the energy consumption for both appliances.
This made it easy to directly compare the energy used by the two devices and conclude that the TV uses more energy than the toaster in their respective operating times.