1. What the heck does that mean???
Homework 18.65
In a “brownout” situation, the voltage supplied by the electric company falls. Assuming the percent drop is small, show that the power output of a given appliance falls by approximately twice that percent, assuming the resistance does not change. How much of a voltage drop does it take for a 60 W light bulb to begin acting like a 50 W light bulb?
This problem has two parts.
(a) Show that the power output of a given appliance falls by approximately twice the percent voltage drop, assuming the resistance does not change.
What the heck does that mean???
(b) Calculate the voltage drop for 60 W bulb to act like 50 W bulb.

2. (a) Show that the power output of a given appliance falls by approximately twice the percent voltage drop, assuming the resistance does not change.
Let me do this first, and then maybe you’ll see what it means. I don’t think I’ll give a problem like this on the exam!
Even though your home power is ac rather than dc, we will use our dc equations, as we have done throughout chapter 18.
OSE: P = V2 / R
Assume the voltage starts at some initial value Vi and decreases by an amount V = Vf – Vi.
The fractional drop is V /Vi and the percentage drop is 100 V /Vi.

3. assuming R does not change
Using P = V2 / R, we get
Pi = Vi2 / R
Pf = Vf2 / R = (Vi - V)2 / R
The power ratio is
assuming R does not change

4. According to the binomial theorem (see page 1043), for x small,
If V is small compared to Vi, then
The change in power is approximately 2(V/Vi), which is what Giancoli wanted you to prove (except I have expressed the result as a ratio and he expressed it as a percent).
“Do you really expect me to remember this?”
Not for an exam. But I expect you to file this “trick” away in your brain for future reference, because it is used by many disciplines in many situations.

5. (b) Calculate the voltage drop for 60 W bulb to act like 50 W bulb.
If you do the calculation using our OSE’s, you won’t get Giancoli’s approximate result. Instead, using our result of part (a):