Fight the Power and Kirchoff Flips the Switch on Ohm’s Law

In the previous blog, we saw that Georg Ohm produced a relationship between lengths of wire and a voltage source, not the famous Ohm’s Law you are likely familiar with today.  In this blog post, we look at the creation of Joule’s Power Law (of heating).

A Quantitative Path for Power

In 1841, James Prescott Joule created resistors from wires wound around glass rods.  This was two decades after Georg Ohm’s experiments with lengths of wire, and before Ohm’s work was transformed into what we know today.  Joule kept the diameter of the wire constant and varied the number of windings.  He knew the ratio of resistances accurately, even without knowing the actual resistance of each wire.  Joule submerged his wire-wound resistors in water containers and connected them in series with a tangent galvanometer and a voltaic pile (battery).

image2

Joule’s experiment placed a series of wire-round resistors in water baths and recorded the temperature rise.

The result of Joule’s experiment is the familiar relationship between heat, resistance, and current.[1]

[1] Page 202 of Arnold Arons “Teaching Introductory Physics” Section 7.6 https://books.google.com/books?id=HpTuAAAAMAAJ

 

Where Q is the heat delivered to the water, I is the current (as measured with a galvanometer), and R is the resistance of the wire-wound resistor.  

 

Joule’s experiment is independent of Ohm’s experiment.  As Arons points out: “The subtle logic of these insights should be carefully noted: There is no a priori reason why all the work done in displacing electrical charge should be converted [completely] into internal thermal energy of the system.  In fact, there are many instances (e.g., the electric motor) where this is not what happens.  In the purely resistive circuit, however, all the electrical work supplied is converted into internal thermal energy.”

Ohm’s Law As We Know It Today

It wasn’t until 1849 that Gustav Kirchoff rewrote the findings of Ohm’s experiment by realizing that τ is current, a is ∆V, and b+x is the resistance of the system R.

Where I is current, V is the potential difference, and R is resistance.  

Kirchoff introduced the current version of Ohm’s Law, not Georg Ohm. Devices that show a direct-proportional relationship between potential difference and the product of current and resistance are termed “ohmic.”

Importance

Ohm’s law shows a direct-proportional relationship between current and potential difference – it intercepts the graph at (0,0).  That means there is no minimum potential difference required to create a current in a conductor.  

Separate from that finding, Joule’s Law shows that all of the work done to displace charge carriers in a purely resistive circuit goes increases the internal energy of the conductor.  There’s no reason that has to be the case, it’s just what nature deems so.  But that finding has nothing to do with Ohm’s law.  The two findings were developed independently.

Hopefully, you made it through high school with hands-on physics experience that prepared you for college physics.  But, there is a greater chance that your high school educational experience was like millions of other students.  Your first experience with electricity was likely limited to a few lecture demonstrations in electrostatics that appeared closer to a magic show than a demonstration of ideas that built to a deep phenomenological understanding.  

After that, there was an abrupt transition from electrostatics to the study of ohmic conductors, perhaps with experiments with a few small light bulbs.  After that, what follows depends largely on the equipment available at the school.  But usually, there is so little equipment, and it is in such a state of disrepair that there are few hands-on labs, and instructors are left to show videos of experiments or use online simulations.

College physics should hopefully rectify many of the shortcomings of the current educational system.  But just in case it didn’t, or in case you could do with a refresher, or perhaps even a new way to look at things, I hope you enjoy (from an academic perspective) the lessons that follow.

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