Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R100, R60 and R40, ....... respectively, the relation between these resistances is

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Question

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R₁₀₀, R₆₀ and R₄₀, ....... respectively, the relation between these resistances is

$\frac{1}{R_{100}} = \frac{1}{R_{40}} + \frac{1}{R_{60}}$

$\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$

R₁₀₀ = R₄₀ + R₆₀

R₁₀₀ > R₆₀ > R₄₀

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$Rated power = \frac{V^{2}}{R}$

$R \propto \frac{1}{Rated power}$

P₁ > P₂ > P₃

_{$∴ \frac{1}{R_{1}} > \frac{1}{R_{2}} > \frac{1}{R_{3}}$}

_{$\frac{1}{R_{100}} > \frac{1}{R_{60}} > \frac{1}{R_{40}}$}