Efficiency of Electrical Appliance

Efficiency of Electrical Appliance

1. The efficiency of an electrical appliance is given by the following equation $$\text{Electrical efficiency = }\frac{\text{useful power output}}{\text{power input }}\times 100\%$$
2. Normally, the efficiency of an electrical appliance is less than 100% due to the energy lost as heat and the work done against friction in a machine.

Example 1
A lamp is marked “240V, 50W”. If it produces a light output of 40W, what is the efficiency of the lamp?

Answer:
$$\begin{array}{l}Efficientcy=\frac{P_{output}}{P_{input}}\times 100\%\\ Efficientcy=\frac{40}{50}\times 100\%=80\%\end{array}$$

Example 2
An electric motor raises a mass of 2kg to a height of 5m in 10s. If the input current from a source of 12V is 2A, find the efficiency of the electric motor.

Answer:
Input power,
$$\begin{array}{l}P=IV\\ P=(2)(12)\\ P=24W\end{array}$$
Output power
$$\begin{array}{l}P=\frac{W}{t}\\ P=\frac{mgh}{t}\\ P=\frac{(2)(10)(5)}{10}=10W\end{array}$$
$$\begin{array}{l}Efficientcy=\frac{P_{output}}{P_{input}}\times 100\%\\ Efficientcy=\frac{10}{24}\times 100\%=41.7\%\end{array}$$