To determine the efficiency of the machine, we need to understand the relationship between input power and output power. Efficiency is a measure of how well a machine converts input energy into useful output energy.
The formula for efficiency ([tex]\( \eta \)[/tex]) is given by:
[tex]\[ \eta = \left( \frac{\text{Power Output}}{\text{Power Input}} \right) \times 100 \% \][/tex]
Here, we are given:
- Power Input ([tex]\( P_{in} \)[/tex]) = 4,000 W
- Power Output ([tex]\( P_{out} \)[/tex]) = 1,900 W
Now, substituting these values into the efficiency formula:
[tex]\[ \eta = \left( \frac{1900 \, \text{W}}{4000 \, \text{W}} \right) \times 100 \% \][/tex]
Calculating the fraction:
[tex]\[ \frac{1900}{4000} = 0.475 \][/tex]
Multiplying by 100 to get the percentage:
[tex]\[ 0.475 \times 100 \% = 47.5 \% \][/tex]
Therefore, the efficiency of the machine is [tex]\( 47.5 \% \)[/tex].
Among the given answer options:
- Efficiency [tex]\( = 2.1 \% \)[/tex]
- Efficiency [tex]\( = 80 \% \)[/tex]
- Efficiency [tex]\( = 195 \% \)[/tex]
- Efficiency [tex]\( = 47.5 \% \)[/tex]
The correct answer is:
[tex]\[ \boxed{47.5 \%} \][/tex]
