Basic formula for Efficiency and How Efficiency is Solved in Cascaded circuits

Generally, efficiency is defined as the ratio of output power to the input power. In Electrical Engineering efficiency is defined in terms of power or energy. Here,

Efficiency (𝞰) = (P_out./P_in) * 100%

Very often in Electrical systems, we come across the cascaded systems. Like the one shown below:

In such cases, the efficiencies should be multiplied to obtain the overall efficiency of the system.

Here in the present case:
𝞰_t = 𝞰₁ * 𝞰₂ * 𝞰₃ * 𝞰₄ 

Example # 1: An electrical tool takes 1000 watt input and provides some output with a loss of 100 watts. Determine the efficiency of the system.

Solution: Input power = Loss + Output power

Output power = 1000 watt - 100 watt = 900 watt

Now efficiency = 900 watt / 1000 watt * 100 = 90%

Example # 2: A power station has three portions. Portion A, Portion B, and Portion C. The efficiencies of portions are 89%, 93%, and 92% respectively. Find the overall efficiency of system.

Solution: 𝞰_t = 𝞰₁ * 𝞰₂ * 𝞰₃ = 0.89 * 0.93 * 0.92 = 0.7614 = 76.14%