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The electric power industry faces much turmoil in the coming decades. The business model of the electric utility company (public or private) may not survive. In addition, the power needs of high-density cities may diverge significantly from non-urban areas causing political turmoil and technical hurdles. The increasing share of renewable energy will be a major…
Power system security is much too big a topic for this article. But I can squeeze in a few points about vulnerability to cyber attacks. First, this topic follows naturally from Part 2’s discussion of grid control (remember that flyball governor?). Second, I feel that’s apropos in an era where the public believes that…
Let me use the terms “power grid” and “network” interchangeably. What is the Power Grid Required to Do? Deliver energy to customers, and thereby earn money so that the utilities can profit. Deliver power wherever and whenever the customers demand it. That implies maintaining the dynamic balance between energy produced, energy lost, and energy…
Instantaneous Power The formula for power is: ##P=V\cdot I## , power= voltage*current. We call that, instantaneous power. Even when ##V## and ##I## are changing in time, ##P=V\cdot I## applies for each instant. It matters not if the ##V## or ##I## changes are `sinusoidal, what their frequency is, or even if they are aperiodic. ##P=V\cdot…
Tell us about your school years? Part of my story is sad but common. I was a poor student. I didn’t pay attention, and I never did homework even once; until one day when it all flipped. That was the day I first learned about differential equations. Diffy-Q was so much fun, that it completely…
If you don’t plan to become a scientist or an engineer, is there a good reason to study physics? I say, “Yes,” because knowing just a little bit can be quite rewarding in ordinary life. For example, I have been enjoying just one little bit of physics for more than 55 years. I even earned…
At first, I wanted this title to say “Ohm’s law is not a Law.” But someone else used that phrase in a recent PF thread, and a storm of protest followed. We are talking about the relationship between Voltage between two points in a circuit and the current between those same two points. ##R=V/I##, or…
Resistance to complex math seems to never die out. I see it frequently in PF posts. Often it takes the form of challenges rather than questions. First challenge: Complex is just a mathematical trick that has nothing to do with the physics. Second challenge: Everything that complex does can be accomplished by ordinary real numbers. …
Introduction Few people know what happens when a customer does something like flipping a light switch. The full explanation requires descriptions of topics that span nanosecond to decade-long time scales. Think of it as scales measured with a high-speed chronograph, a stopwatch, an hourglass, or by a calendar. At the earliest and briefest instants, pure…
This article is the first of a two-part series that presents two distinctly different approaches to parallel programming. In the two articles, I use different approaches to solve the same problem: finding the best-fitting line (or regression line) for a set of points. The two different approaches to parallel programming presented in this and the…
We asked our PF Advisors to tell us their most memorable or influential textbook and why. Here are their responses… Thanks to all the PF Advisors that shared their favorite textbook. We have more questions for them in the near future. Stay tuned for another “Ask the Advisors”!
Probably everyone reading this article already has education on elementary circuit analysis (CA) and many of us are much more advanced. Typically, the basic course covers both circuits covers simple devices like R, L, and C, it mentions electric or magnetic fields, then moves on to Ohm’s Law and CA… But few such courses explicitly…
Give us a little background on Jim Hardy Born and raised in Miami Florida of parents with roots in Springfield Missouri . So at heart i’m a small town midwestern fellow. Miami was small in the 1950’s but it became cosmopolitan and outgrew me. I spent a career working in the nuclear plant south of…
We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45 degrees. Many quantitative results can be read off a spacetime diagram simply by counting boxes, with very little algebra—I like to describe this as a method for doing “visual calculations” in relativity. The details are…
This Insight is part of our “Young Authors” series, where talented young students showcase their knowledge. This is how both you and I learned it back in elementary school. $$5^3 = 5*5*5$$ Using this you can raise anything to any power- as long as that power is a whole number. What about fractions and negative…