Question

Lightbulbs labeled $40W,60W$and $100W$ are connected to a$120V/60Hz$power line as shown in the figure .What is the rate at which energy is dissipated in each bulb?

Short answer

The rate at which energy is dissipated in each bulb is

$I=0.2\mathrm{A},{\mathrm{P}}_1=14.4\mathrm{W},{\mathrm{P}}_2=9.6\mathrm{W}$

Step-by-step solution

Given Information

We have been given that light bulbs of $40W,60Wand100W$are connected to a $120V/60Hz$powerline and we have to find the rate at which energy is dissipated in each bulb.

Simplification

For the bulb of $40W$:

$P_1=\frac{V^2}{R_1}$

For the $60W$bulb:

$P_2=\frac{V^2}{R_2}$

$R_2=240\Omega$

The total resistance is:

$600ohm$

The power dissipation in $40W$bulb is:

$P_{di{s}_1}=14.4\mathrm{W}$

The power dissipation in bulb is:

$P_{di{s}_2}=9.6\mathrm{W}$