The supply voltage to an electric room heater decreases by 2.5 % . Assuming the resistance of the heating element remains constant, what is the approximate percentage decrease in the power consumed by the heater?

Step-by-step solution

The power consumed by an electric heater is given by P = V^2 R , where V is the supply voltage and R is the constant resistance of the heating element. Taking the natural logarithm on both sides, we get: P = 2 V - R Differentiating for small changes, we obtain the fractional change in power: P P = 2 V V Converting to percentage change: % change in P = 2 ( % change in V) Given that the supply voltage decreases by 2.5 % , the approximate percentage decrease in power consumed is: % decrease in P = 2 2.5 % = 5.0 % Assu