Two electric bulbs have the following specifications.
- 100W at 220V.
- 1000W at 220V.
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The resistance of filament,
$\text{R}=\frac{\text{V}}{\text{I}}=\frac{\text{V}^2}{\text{P}}$
At constant voltage V, the resistance,
$\text{R}\propto\frac{1}{\text{p}}$
That is the resistance of filament of 100W bulb is greater than that of 1000W bulb.
The ratio of resistances $=\frac{\text{R}_1}{\text{R}_2}=\frac{\text{P}_2}{\text{P}_1}$
$=\frac{1000}{100} $
$=\frac{10}{1}=10:1$
$\text{R}=\frac{\text{V}}{\text{I}}=\frac{\text{V}^2}{\text{P}}$
At constant voltage V, the resistance,
$\text{R}\propto\frac{1}{\text{p}}$
That is the resistance of filament of 100W bulb is greater than that of 1000W bulb.
The ratio of resistances $=\frac{\text{R}_1}{\text{R}_2}=\frac{\text{P}_2}{\text{P}_1}$
$=\frac{1000}{100} $
$=\frac{10}{1}=10:1$
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