To determine the efficiency of a DC generator, you can use the formula for efficiency, which is given as:
[tex]\[ \text{Efficiency} (\eta) = \left( \frac{\text{Output Power}}{\text{Input Energy}} \right) \times 100\% \][/tex]
Here, we are provided with the following information:
- The input energy required by the DC generator: 100 watts
- The output power supplied by the DC generator: 80 watts
Now, let's calculate the efficiency step-by-step using the formula mentioned above.
1. Identify the input energy ([tex]\(E_{\text{in}}\)[/tex]):
[tex]\[ E_{\text{in}} = 100 \text{ watts} \][/tex]
2. Identify the output power ([tex]\(P_{\text{out}}\)[/tex]):
[tex]\[ P_{\text{out}} = 80 \text{ watts} \][/tex]
3. Substitute the values into the efficiency formula:
[tex]\[ \eta = \left( \frac{P_{\text{out}}}{E_{\text{in}}} \right) \times 100\% \][/tex]
[tex]\[ \eta = \left( \frac{80 \text{ watts}}{100 \text{ watts}} \right) \times 100\% \][/tex]
4. Simplify the fraction:
[tex]\[ \eta = \left( 0.8 \right) \times 100\% \][/tex]
5. Multiply by 100%:
[tex]\[ \eta = 80\% \][/tex]
Thus, the efficiency of the DC generator is 80%.
Therefore, the correct answer is:
B. 80%
