Question

A desk lamp that plugs into a wall socket can use a or a light bulb. Which bulb has the larger resistance? Explain briefly.

Short answer

The bulb has the larger resistance.

Step-by-step solution

Given data

Input voltage:

$V=120V$

Output power of first bulb:

$P_1=60W$

Output power of second bulb:

$P_2=100W$

Resistance of a bulb

The resistance of a bulb of wattage when connected to an input voltage is

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

Determination of resistances of the two bulbs

From the above equation, the resistance of the first bulb is:

$$\begin{gathered} R_1=\frac{V^2}{P_1} \\ =\frac{{\left(120V\right)}^2}{60W} \\ =240.\left(1V^2/W\times \frac{1\mathrm{\Omega }}{1V^2/W}\right) \\ =240\mathrm{\Omega } \end{gathered}$$

From the above equation, the resistance of the second bulb is:

$$\begin{gathered} R_2=\frac{V^2}{P^2} \\ =\frac{{\left(120V\right)}^2}{100W} \\ =144.\left(1V^2/W\times \frac{1\Omega }{1V^2/W}\right) \\ =144\Omega \end{gathered}$$

Thus, the first bulb has the larger resistance.