The electric bulbs have tungsten filaments of same length. If one of them gives $60 \,watt$ and other $100\, watt$, then
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a
${P_{Rated}} \propto \frac{1}{R}$ and $R \propto \frac{1}{{{{{\rm{(Thickness }}{\kern 1pt} {\rm{of}}\,{\rm{filament)}}}^{\rm{2}}}}}$
${P_{Rated}} \propto \frac{1}{R}$ and $R \propto \frac{1}{{{{{\rm{(Thickness }}{\kern 1pt} {\rm{of}}\,{\rm{filament)}}}^{\rm{2}}}}}$
So ${P_{Rated}} \propto {({\rm{Thickness}}\,{\rm{of}}\,{\rm{filament)}}^{\rm{2}}}$
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