Question

An engine delivers 1000 watt of power with 80% efficiency. The input power is

• A. 800 W
• B. 1000 W
• C. 1250 W
• D. 1500 W

Hint:

Remember that efficiency is always less than 1 (or 100%). Therefore, the input power must always be greater than the output power, as some energy is always lost (usually as heat). This can help you eliminate options like 800 W and 1000 W immediately.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the output power of an engine and its efficiency. We need to calculate the power that is supplied to the engine, which is the input power.

Step 2: Key Formula or Approach:
The efficiency (\(\eta\)) of an engine is defined as the ratio of the useful output power to the total input power, usually expressed as a percentage.
\[ \eta = \frac{\text{Output Power}}{\text{Input Power}} \]
To find the input power, we can rearrange this formula:
\[ \text{Input Power} = \frac{\text{Output Power}}{\eta} \]

Step 3: Detailed Explanation:
Given values are:
- Output Power = 1000 W
- Efficiency, \(\eta = 80\% = \frac{80}{100} = 0.8\)
Using the rearranged formula to find the Input Power:
\[ \text{Input Power} = \frac{1000 \text{ W}}{0.8} \]
\[ \text{Input Power} = \frac{10000}{8} \text{ W} \]
\[ \text{Input Power} = 1250 \text{ W} \]

Step 4: Final Answer:
The input power required for the engine is 1250 W.