In electrical energy calculations, 1 watt hour (1 Wh) is equal to how many joules of energy?

Introduction / Context:
Electric energy consumption is often expressed in units such as watt hour and kilowatt hour on electricity bills. In physics, the joule is the SI unit of energy. Converting between watt hour and joules is a common task when solving numerical problems about electrical appliances, power ratings, and energy usage. This question focuses on the basic conversion for 1 watt hour.

Given Data / Assumptions:

• Power P in watts is defined as energy per unit time, P = E / t.
• 1 watt equals 1 joule per second.
• 1 hour equals 3600 seconds.
• We want energy corresponding to 1 watt used for 1 hour.

Concept / Approach:
A watt hour is the energy consumed by a device that uses one watt of power for one hour. Since watt is joule per second, multiplying by time in seconds gives energy in joules. Therefore, 1 Wh equals 1 W multiplied by 1 hour in seconds. Knowing that 1 hour equals 3600 seconds, the calculation becomes straightforward: 1 Wh = 1 J/s times 3600 s, giving 3600 J. This relationship is the basis for scaling up to kilowatt hours, where 1 kWh equals 3.6 million joules.

Step-by-Step Solution:
Step 1: Start with the definition of power: P = E / t, so E = P * t. Step 2: For 1 Wh, take P = 1 watt and t = 1 hour. Step 3: Recall that 1 watt = 1 joule per second, so 1 W = 1 J/s. Step 4: Convert 1 hour to seconds: 1 hour = 60 minutes and 1 minute = 60 seconds, so 1 hour = 60 * 60 = 3600 seconds. Step 5: Calculate energy: E = (1 J/s) * 3600 s = 3600 J.

Verification / Alternative check:
As a cross check, consider a 100 W bulb running for 10 hours. In watt hour, energy is 100 W * 10 h = 1000 Wh, which is 1 kWh. In joules, that should be 1000 * 3600 J = 3.6 * 10^6 J. Textbook values confirm that 1 kWh equals 3.6 megajoules. Dividing by 1000 returns 3600 J per 1 Wh, confirming the conversion factor.

Why Other Options Are Wrong:
360 joules: This is smaller by a factor of 10 and does not match the correct conversion. 36000 joules: This is larger by a factor of 10 and therefore incorrect. 36 joules: This is off by a factor of 100, far from the correct value.

Common Pitfalls:
A common mistake is to forget that there are 3600 seconds in an hour, leading to errors by factors of 60 or 600. Another confusion arises between watt hour and kilowatt hour, which differ by a factor of 1000. Remember the basic chain: 1 W = 1 J/s, 1 h = 3600 s, so 1 Wh = 3600 J, and 1 kWh = 3.6 * 10^6 J.

Final Answer:
One watt hour is equal to 3600 joules of energy.