## Ohm From Ohm

Amongst the myriad inconveniences and troubles of a Physics teacher’s life, the choice of the symbols commonly used to represent voltage, current and resistance, must surely rank in the top ten.

### V is for voltage in volts, V

Well, OK, that’s sensible enough. On a good day, I may even remember to call it “potential difference”. The sage advice of Never use two words when one will do is commonly accepted by everyone; however, Physics teachers have, as a profession, decided to go it alone and completely ignore this tired old saw. Thus, voltage is become potential difference because of — erm, reasons (?)

One can only hope that everyone got the memo . . .

### R is for resistance in ohms, Ω

R for resistance? That’s fairly sensible too.

“But what’s that weird squiggly thing, Sir?”

“Ah, you mean the Greek letter omega? Because Physics is soooo enormous that the measly 26 letters of the Latin alphabet ain’t big enough for it…”

### I is for current in amps, A

“WTφ? Are you taking the πΣΣ, Sir?”

“I know, I know! Look, if it helps, think of it as short for intensité du courant . . . Wait, don’t leave! Stop, I have many more fun Physics facts to teach you! Look, here’s a picture of Richard Feynman playing his bongo drums — nooooooooo!”

# V = I R

Except, that’s not Ohm’s Law; it’s actually the definition of resistance:

# R = V / I

There is not a single instance where it is not true by definition. The value of resistance will always be equal to the ratio of the potential difference and the current.

Think of it like this. At room temperature, 1 V of potential difference can push (say) 0.5 A of current through the wire in a filament bulb. (I just love that retro 1890s tech, don’t you?)

This means it has a resistance of 1/0.5 = 2 ohms. However, bump up the potential difference to 6 V and the current is (say) 0.75 A. This means that is has a resistance of 6/0.75 = 8 ohms. Its resistance has changed because it has become hotter. In other words, its resistance is not constant.

Ohm’s Law is perhaps most simply stated as:

The potential difference is directly proportional to the current over a range of physical conditions (including temperature).

Using standard symbols:

# V α I

or, taking R’ as a constant of proportionality:

# V = I R’

You do see the difference, don’t you?

In the first example, R is not a constant value for a given range of physical conditions: for example it can get higher as the temperature increases.

In the second, R’ is constant over a range of temperatures and other physical conditions.

And so there we have it: V=IR can be a perfectly valid statement of Ohm’s Law, provided it is specified that R is constant. If one does not do that, then all bets are off…

In the meantime, here’s another picture of Richard Feynman playing the bongo drums. Enjoy!

### 6 thoughts on “Ohm From Ohm”

1. howardat58 May 11, 2018 / 10:34 pm

It’s time to brush off the dust and get out the moving coil meter !

• e=mc2andallthat May 11, 2018 / 10:37 pm

You let your moving coil meters gather dust? Shame on you! Such wonderful tech should never be allowed to fall into undeserved desuetude. Now all I need is someone to teach me how to use a slide rule…

2. paulmartin42 May 12, 2018 / 11:37 am

Just checked my new bible (Ben Rogers, Big Ideas in Physics) and in chap 1: Electricity, no Ohm’s Law & though it is useful that you have pointed out the omission I think his emphasis is correct if your are a Physics person. And engineer though is concerned with practicalities (eg 42R) – Ohm’s Law is History, as you have demoed

• paulmartin42 August 26, 2021 / 8:21 am

Physics Girl
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Lesson 19 (Voltage, Resistance and Current) of Dianna’s Intro Physics Class on Physics Girl. Never taken physics before? Want to learn the basics of physics? Need a review of AP Physics concepts before the exam? This course is for you!

Worth a watch … from Jan 2021