Archive for Electricity

Moving Over

Posted in Biographical, Covid-19, Maynooth with tags , , on September 18, 2020 by telescoper

Although I moved into my new house in Maynooth nearly three weeks ago, it was only today that my former landlord came to collect the keys to the flat I was formerly living in. I am quite pleased that I no longer have the keys because having them made me feel some sort of responsibility for the place even though there is nothing of mine there. Handing over the keys is a form of closure, I suppose.

The fact that the landlord wasn’t in a hurry to complete the formalities gave me a bit of extra time to finish a couple of tasks that took longer than I’d expected.

The first was to close the electricity account for which task I needed a final reading from the electricity meter. One of the awkward things about the flat I was in was that the electricity meter isn’t in the flat but in a cupboard in the hallway along with the meters for the other three flats in the building. The cupboard belongs to the management company and they have the only keys. Whenever I needed a meter reading I therefore have to ask them to take one. I contacted them before moving out to do this, but they only sent me the reading this Monday so I only just got the account closed this week. I was a bit irritated that it took so long, but pleased in the end because the reading was substantially less than the `estimated’ reading used by the electricity company in the absence of any readings during the lockdown so I got a nice farewell refund.

Incidentally, the level of sloth of managing agents is by no means unusual in my experience. They always seem to manage to do as little as possible.

The other thing was the washing machine. The appliance supplied with the flat broke down at the start of the lockdown so I bought a new one just in time before all the stores closed and, with the landlord’s permission, I scrapped the old one. I always had the intention of taking the new one with me when I moved out. When the time came however it proved more difficult than I’d imagined.

In order to detach a washing machine from the water supply it is necessary to close a valve, otherwise there will be a flood. Unfortunately the valve was jammed and I could budge it. No worry, I thought, I’ll just turn off the cold water at the stopcock. Mostly this is found under the kitchen sink but when I looked for it I realized that whoever had installed the unit under the sink had boarded up the stopcock so it was inaccessible. I therefore had to take the back panel off the unit to get at the stopcock. When I had done that I found the stopcock wouldn’t budge. Not at first anyway. Eventually, with the application of a bit of elbow grease, I got it to turn. And so it came to pass that the washing machine was detached.

I then had to cart it to my new house. The only hard bit of that was lifting the thing onto the trolley I’d borrowed for the purpose. Washing machines are rather heavy, you see. After some struggling I managed to get going and trundled quite happily down the road to my new house and got it attached to the water there without any problem.

After having a cup of tea and a bit of a rest I thought it would be a good idea to go back to the flat and leave a note to explain that the cold water was turned off at the main and that it would be inadvisable to turn it on without sealing up the inlet pipe with a blank (or indeed another washing machine).

These tasks completed, and the keys returned, one part of the process of moving is now over. Phase Two will involve transporting the rest of my belongings from Cardiff, but that won’t be possible for a while as it looks like both Ireland and the UK are heading for more restrictions on movement due to Covid-19.

The one thing that has really struck me since moving is how much quieter my new neighbourhood is. The flat was on a main road so – apart from the full lockdown period in the spring – there was constant traffic noise. Although I got used to it, it did make it very hard to record video lectures etc. The new place is sufficiently far from large roads that the background noise is negligible, and it’s a detached house so there’s no noise from the neighbours either!

The Solution

Posted in Cute Problems with tags , , on February 24, 2010 by telescoper

A few days ago I posted a little puzzle about the resistance measured between two adjacent nodes in an infinite square grid made of of 1Ω resistors. There was a bit of discussion after the post that hinted at the solution but, since a few people have asked me about it, I thought I’d post a fuller answer here.

The quickest way I know to get the answer uses the Principle of Superposition, as illustrated in the following picture.

Consider two copies of the grid, both earthed at infinity. Imagine injecting a current of 1 Amp into the grid through a wire attached to node A as shown in the top left of the picture. The current will run to earth through the grid, but, by symmetry, it is obvious that 1/4 of the current entering the grid through A must travel through each of the 4 wires radiating out from it. Each of the wires leading out from A therefore carries 0.25 Amps in this solution.

Now, in the top right hand picture, forget about A, but attach a wire to B and pull out 1 Amp from the earth (at infinity). By a similar argument to the first diagram, 0.25 Amps must be flowing into B along each of the wires connected to it in the directions shown.

We now have two perfectly good solutions for currents flowing in resistive networks. The principle of superposition says that if we add the two solutions we also get a solution. Adding the two configurations above means that the resistor joining A to B must be carrying 0.5 Amp (0.25 from the first solution and 0.25 from the second, both in the same direction). But this is a 1Ω resistor so the Voltage across AB must be 0.5 V.

Now think of the whole mesh as being a black box in between the input wire and output wire. This black box has a current of 1 Amp flowing through it and the voltage dropped is 0.5 V. It’s resistance is therefore 0.5 Ω.

If anyone has a better solution than this, I’d like to see it!!