Question

The specification on a heater coil is 250 V, 500 W. Calculate the resistance of the coil. What will be the resistance of a coil of 1000 W to operate at the same voltage?

Answer 1

Let R be the resistance of the coil.
The power P consumed by a coil of resistance R when connected across a supply V is given by
$$\begin{gathered} P=\frac{V^2}{R} \\ \Rightarrow R=\frac{V^2}{P} \\ \Rightarrow R=\frac{{\left(250\right)}^2}{500}=125\mathrm{\Omega } \end{gathered}$$

Now, P = 1000 W
$\Rightarrow R=\frac{V^2}{P}=\frac{{\left(250\right)}^2}{1000}=62.5\mathrm{\Omega }$