Question

A 2-way light bulb for a 110. V lamp has filament that uses power at a rate of 50.0 W and another filament that uses power at a rate of 100. W. Find the resistance of these two filaments.

Answer 1

Given:

The potential difference is,

$V=110\text{ V}$

The power of the first filament is,

$P_1=50.0\text{ W}$

The power of the second filament is,

$P_2=100\text{ W}$

To find:

resistance of these two filaments

Explanation:

The power of the filament is,

$P=\frac{V^2}{R}$

The resistance of the first filament is,

$\begin{gathered} R_1=\frac{V^2}{P} \\ =\frac{110\times110}{50.0} \\ =242\text{ ohm} \end{gathered}$

The resistance of the second filament is,

$\begin{gathered} R_2=\frac{110\times110}{100} \\ =121\text{ ohm} \end{gathered}$

Hence, the resistances of the filaments are 242 ohms and 121 ohms.