Question

The power $P$, in watts, of an electrical circuit varies jointly as the resistance $R$ and the square of the current $I$. For a $240-watt$ refrigerator that draws a current of $2$ amperes, the resistance is $60ohms$. What is the resistance of a $600-watt$ microwave oven that draws a current of $5$ amperes?

Answer 1

It is given that the power $P$ varies jointly as the resistance $R$ and the square of the current $I$ and $P=240$ watt when $R=60$ ohms and $I=2$ amperes, therefore,

$P=kR{I}^2\Rightarrow 240=k\times 60\times {\left(2\right)}^2\Rightarrow 240=k\times 60\times 4\Rightarrow 240k=240\Rightarrow k=\frac{240}{240}=1$

Thus, the general equation is $P=R{I}^2$.

Since $P=600$ watt and $I=5$ amperes, therefore,

$P=R{I}^2\Rightarrow 600=R{\left(5\right)}^2\Rightarrow 25R=600\Rightarrow R=\frac{600}{25}=24$

Hence, the resistance of a $600$ watt microwave oven that draws a current of $5$ amperes is$24$ ohms.