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

A. 1/R100 = 1/R40 + 1/R60
B. R100 = R40 + R60
C. R100 > R60 > R40
D. 1/R100 > 1/R60 > 1/R40

To solve this problem, let's first understand the relationship between power, resistance, and temperature in incandescent bulbs.

The power of an incandescent bulb is given by the formula:

P = V² / R,

where:

P is the power of the bulb,
V is the voltage across the bulb,
R is the resistance of the filament.
At room temperature, the filament resistances of the 100 W, 60 W, and 40 W bulbs are denoted by R100, R60, and R40, respectively.

Since power is inversely proportional to resistance (for a constant voltage), a higher power rating implies a lower resistance. Therefore, the relationship between the resistances at room temperature can be deduced as:

R100 < R60 < R40.
This means that the 100 W bulb has the least resistance, the 60 W bulb has a medium resistance, and the 40 W bulb has the greatest resistance at room temperature.

Now let's analyze the given options:

A. 1/R100 = 1/R40 + 1/R60
This is incorrect because the power ratings do not follow such a reciprocal relationship between resistances.

B. R100 = R40 + R60
This is incorrect because it suggests a simple additive relationship between resistances, which is not correct in this context.

C. R100 > R60 > R40
This is incorrect because, as established earlier, R100 < R60 < R40, not the other way around.

D. 1/R100 > 1/R60 > 1/R40
This is correct. Since R100 < R60 < R40, their reciprocals will follow the reverse order: 1/R100 > 1/R60 > 1/R40.

Thus, the correct answer is:

D. 1/R100 > 1/R60 > 1/R40.