Mr Ohm and the Coffee Technician

Once upon-a time back in the 1780’s, an Ohm had nothing to do with electrical circuits. An Ohm was just a member of a German Family, Dad was a hard working locksmith and mum a cheese maker house wife. But soon this poor family would be more famous than their Lederhosen trousers. Because their son Georg Simon Ohm, would become the father of the electrical circuit. So famous would he become, he got his own symbol. And all this despite there being a lot of resistance to his ideas. See what I just did there!

So what did this mathematician school teacher come up with and how is it relevant to a coffee machine repair. Not long after his return from Mount Sinai, Mr Ohm stated let V = I × R

V is the voltage across the circuit elements.
I is the current flowing through the circuit.
R is the resistance of the circuit.

From this equation we can derive further useful things like power(Watts), see the Ohms wheel below;

Now I know what you’re thinking, you dont need this for a coffee machine repair. Well actually you do, an example is determining the wattage of a replacement element or thermoblock. Usually they are engraved, but not always. So assuming 240V is the operating voltage, all we need is the resistance Ohms and we can calculate the wattage of the element using P=V2/R.

Ohms Law has implications for resisters in parallel and Series, the latter is easy  as resisters in series just add together but resisters in parallel offer alternate path for current to flow, often called a current divider.

Suppose we have a circuit of voltage V and current I. The resistors R₁, R₂ and R₃ are connected in parallel to the circuit. It is known that in a parallel circuit, the current gets divided into number of parts which is equal to the number of resistors.

Let I₁, I₂ and I₃ be the values into which the current I gets divided. We know,

I = I₁ + I₂ + I₃

Dividing both sides by V we get,

I/V = I₁/V + I₂/V + I₃/V

1/(V/I) = 1/(V/I₁) + 1/(V/I₂) + 1/(V/I₃)

According to Ohm’s law, V = IR. So, the above equation becomes,

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

This derives the formula for equivalent resistance in a parallel circuit.

Ohms Law has relevance for testing the Delonghi Thermoblocks, one of which is composed of 2 elements(resistors) in parallel.

In the first photo I am testing the flash boiler (horse shoe one). I got 54 ohms, which is what I expected. How did I know this, I used ohms law, on the boiler it says 1000W @ 230V, not in those  precise words. I know from the equation Resistance=Volts squared over Power,  so 230V squared divided by 1000W = 52.9 ohms. That’s close enough.

The next photo shows me testing the main generator element. I got 80 ohms. The element is marked 230V, 600W, so I calculate 88 ohms. Again close enough.

However please note the above result I obtained by testing the elements separately, there are 2 elements wired in parallel in the Delonghi machine. So if you just test the top element with the wires connected to the top element as the picture below shows, you should get 40 ohms not 80 ohms as resistance in parallel halves the total resistance. If you get 80 odd ohms then either a fuse is out to one element or the element is out. So this test is easy as you do not have to dig for the second element or thermal fuses in order to tell instantly if all is well with the thermoblock.

That’s a little of Ohms Law in action and assisting us with a coffee machine repair.