First slide

Thermal effect of current

Question

A 500 W heating unit is designed to operate from a 115 Volt line. If the line voltage drops to 110 volt. The percentage drop in heat output will be

Easy

A

10.20 %
B

8.1 %
C

8.6 %
D

7.6 %

Solution

$w e k n o w P = \frac{V^{2}}{R} \begin{array}{l} ∴ \frac{P^{1}}{P} = \frac{V^{1^{2}}}{V^{2}} \\ \Rightarrow \frac{P^{1}}{P} = {(\frac{110}{115})}^{2} = {(1 - \frac{5}{115})}^{2} \\ u \sin g b i n o m i a l a p p r o x \\ \Rightarrow \frac{P^{1}}{P} = 1 - \frac{10}{115} = 1 - \frac{2}{23} \\ \Rightarrow \frac{P^{1}}{P} - 1 = - \frac{2}{23} \\ m u l t i p l y i n g b o t h s i d e s w i t h 100 w e g e t \\ \Rightarrow (\frac{P^{1}}{P} - 1) \times 100 = - \frac{200}{23} = - 8.6 % \end{array}$

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