Incandescent bulbs are designed by keeping in mind that resistance of their filament increases
with the increase in temperature. If at room temperature,$100{\rm{W}}$,${\rm{60W}}$and
$40{\rm{W}}$bulbs have filament resistances ${{\rm{R}}_{{\rm{100}}}}$,
${{\rm{R}}_{60}}$and${{\rm{R}}_{40}}$respectively, the relation between the resistance is
A. $\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{100}}}}}}{\rm{ =
}}\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{40}}}}}}{\rm{ +
}}\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{60}}}}}}$
B. ${{\rm{R}}_{100}}{\rm{ = }}{{\rm{R}}_{40}}{\rm{ + }}{{\rm{R}}_{60}}$
C. ${{\rm{R}}_{100}}{\rm{ > }}{{\rm{R}}_{60}}{\rm{ > }}{{\rm{R}}_{40}}$
D. $\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{100}}}}}} >
\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{60}}}}}} >
\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{40}}}}}}$

Hint: From the concept of power and deriving the formula for power of electric circuit, which is
given by ${\rm{P}} = \dfrac{{{{\rm{V}}^{\rm{2}}}}}{{\rm{R}}}$ where ${\rm{V}}$is the
voltage.
The rate at which energy is absorbed or produced within a circuit is electrical power, (P) in a
circuit. The quantity symbol for power is P, and is the voltage product multiplied by the current
with the measuring unit being Watt (W).
Complete step by step solution:
An incandescent bulb is a bulb that produces light when its filament gets heated and it glows. It
is also known as incandescent lamp as well as incandescent light globe. A filament is a thread
like conducting wire that is made up of metal with high melting point and is closed inside a bulb
to protect it from oxidation. These bulbs are of very low efficiency than other types of electric
lighting devices.
In the above problem the circuit with the same voltage is written.

Therefore,
${\rm{P}} \propto \dfrac{{\rm{1}}}{{\rm{R}}}$
Here, ${\rm{R}}$is the resistance.
Now, Circuit with high wattage is written in descending order as the resistance of their filament
increases with the increase in room temperature.
$100{\rm{W}} > {\rm{60W}} > {\rm{40W}}$
Therefore,
${{\rm{P}}_{{\rm{100}}}} > {{\rm{P}}_{{\rm{60}}}} > {{\rm{P}}_{{\rm{40}}}}$
As the power of the bulb is directly proportional to its resistance
Hence,
$\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{100}}}}}} >
\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{60}}}}}} >
\dfrac{{\rm{1}}}{{{{\rm{R}}_{{\rm{40}}}}}}$
Resistance can be defined as the measurement of the opposing force offered to the current to
flow in an electrical circuit. It is measured in ohms. It electrical circuits resistors are installed to
resist the flow of electric current.
Note: These bulbs have a very short life, produce a lot of heat and require a lot of power
compared to other LEDs.