How Much Power is Dissipated by a Lightbulb with Corroded Socket Contacts?

[Snazzy]

Homework Statement

The corroded contacts in a lightbulb socket have 5.0 Ohms of resistance. How much actual power is dissipated by a 100 W (120 V) lightbulb screwed into this socket?

Homework Equations

P = V^2/R
V = IR
P = RI^2

The Attempt at a Solution

I found the resistance of the lightbulb to be 120^2/100 = 144 Ohms, then added 5 Ohms to it to get the resistance of the entire circuit. Then I found the current in the circuit by using I = V/R = 0.8054 A, and then I found the power dissipated by the lightbulb by using P = R(of the lightbulb)I^2 = 144 x 0.8054 = 93.4 W as my final answer, but I don't know if this is right and electric circuit analysis is NOT my specialty in physics.

 

[kamerling]

This is completely right, and clearly explained!