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

Engineering

Physics

Heating Effects of Current and Electric Power

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 R₄₀respectively, 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 > R₆₀ > R₄₀

R₁₀₀ = R₄₀ + R₆₀

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

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

P₁ > P₂ > P₃

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

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