Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. At room temperature,$100\mathrm{W}$, $60\mathrm{W}$, and$40\mathrm{W}$ bulbs used in circuits with the same voltages will have filament resistances as____ 

$V=\frac{V^2}{R}$, where Vis is the voltage, is the formula for the power of an electric circuit that is derived from the idea of power.
Electrical power, abbreviated as P in a circuit, is the rate at which energy is consumed or generated inside a circuit. Power is represented by the quantity symbol P, which is equal to the voltage product times the current, with the unit of measurement being the watt (W).

A bulb that emits light as its filament heats up and glows is known as an incandescent bulb. Both incandescent lamp and incandescent light globe are other names for it. A filament is a conducting wire that resembles a thread and is enclosed inside a bulb to prevent oxidation. It is constructed of metal with a high melting point. When compared to other forms of electric illumination, these bulbs have an extremely poor efficiency.
The identical voltage circuit is written in the problem mentioned above.
Therefore,

$⟹P\propto \frac{1}{R}$

Ris is putting up a fight here.
Now since the resistance of their filaments is increasing with the rise in room temperature, circuits with high wattages are written in declining sequence.
$100 \mathrm{W}>60 \mathrm{W}>40 \mathrm{W}$
Therefore,

$⟹P_{100 }>P_{60} >P_{40}$

Because the bulb's wattage is precisely proportional to its resistance,

$\frac{1}{{\mathrm{R}}_{100}}>\frac{1}{{\mathrm{R}}_{60}}>\frac{1}{{\mathrm{R}}_{40}}$

The measurement of the force put up to prevent current from flowing in an electrical circuit is known as resistance. Ohms are used to measure it. Resistors are used in electrical circuits to impede the passage of electricity.

Hence, the correct answer is option A.