So, this gem comes from my MCAT test prep material. Though it is sufficient to make me demand my money back, I’m more concerned about the tomfoolery that ensued when I shared it with my fellow engineer-friends, for it does not bode well for me.
“Two light bulbs, one 60 watt bulb (higher resistance) and one 100 watt bulb (lower resistance), are placed in series. A current is run through them. Which bulb glows brighter?”
It’s a fair question, one of basic circuit theory. In series, both bulbs experience the same current. After that, it’s Ohm’s Law. The bulb with higher resistance–the 60 watt bulb–experiences a greater voltage drop across it than the bulb with lower resistance, thus dissipating more power and glowing brighter.
Though this information is given, one can justify the higher/lower resistance of the bulbs by realizing that the wattage of a bulb is given assuming household voltages (120 V). The relationship V = I * R can be substituted into the power equation, P = V * I, to arrive at P = V2/R. A higher wattage thus implies a lower resistance.
However, the explanation given in my prep material decides to take a different tack:
“…But in series, the bulb with more resistance would draw more current, thus gets more voltage, so the 60 watt bulb glows brighter, has more power.”
I really couldn’t make it past “the bulb with more resistance would draw more current.” O RLY? EPIC FAIL. It was further disappointing to find this exact difficulty documented on the Internet nearly two years ago.
After having vented my initial frustrations on the Face-space and the instant messenger, I shared it with Chuck (a biomedical engineering Ph.D.) and Jeff (a chemistry Ph.D.–but we won’t hold that against him) at work the next day. Now, this question isn’t supposed to spark a whole lot of additional thought: just figure out which bulb glows brighter and select the correct multiple-choice answer. After sharing in my indignation at seeing such an atrocious falsehood in print, Chuck, in his inimitable way, went on to spend the next few minutes filling out an 8.5″x11″ sheet of paper deriving an expression for just how much brighter the 60 watt bulb would be. (It’s actually a simple relationship, but to derive it from first principles is a fun exercise for someone who hasn’t done it in awhile. And if you’re into that sort of thing, I guess.)
Yes, engineers are dorks. And I could totally see myself doing something silly like that on the test. Apparently a fundamental result of my education that normally works to my advantage is a handicap that must be overcome if I am to have any chance at doing well on this stupid test.
