A 500 ~W heating unit is designed to operate on a 400 ~V line. If line voltage drops to 160 ~V , the percentage drop in heat output will be:

Step-by-step solution

The power P consumed by a heating unit is given by the formula P = V^2 R , where V is the voltage and R is the resistance of the heating element. Since the resistance R is constant, the power is proportional to the square of the voltage, P V^2 . Let P₁ = 500 W at V₁ = 400 V . When the voltage drops to V₂ = 160 V , the new power P₂ is given by: P₂ P₁ = ( V₂ V₁ )^2 Substituting the values: P₂ 500 = ( 160 400 )^2 = ( 2 5 )^2 = 4 25 P₂ = 500 4 25 = 20 4 = 80 W The drop in heat output is P₁ - P₂ = 500 - 80 = 420 W . The