AH investigation report

This week is your last chance to submit a draft of your investigation report for proof reading.  I have already given you a copy of the SQA guidelines for candidates.  You might also find the attached uncertainties document helpful.  Pay special attention to the final page; reports that fail to account for calibration uncertainty will be penalised by the external marker.

If you are struggling with uncertainties in Excel, have a look at the two linest documents I posted earlier this year.

capacitors – charge, energy and graphs

We’ve just completed the topic on capacitors in dc circuits, finishing off with a detailed study of the graphs obtained for current & voltage against time when a capacitor is charged or discharged through a series resistor.  There are some additional notes and practice questions at the end of this post but please watch the clips first.

This introduction to capacitors from the nice people at Make Magazine is a good starting point.

The S-cool revision site has some helpful notes and illustrations on capacitor behaviour; try page 1 (how capacitors work) and page 2 (charging and discharging).

Here is a video that covers some of the areas we discussed in class. Ignore the maths at the end of each section of the film, you won’t need it.  Notice how the man in the film uses a lightbulb, rather than an ammeter, to show when the current is large or small.  Clever, eh?

One use of capacitors you should know about is the flashing lamp.  We’ll cover this application next week.

Blinking Neon Bulb (5F30.60A) from Ricardo Alarcon on Vimeo.

I compared normal electrolytic capacitors to a 10F supercapacitor, and we observed its superior performance in terms of energy storage.  This video goes one step further and shows the fun you could have with an ultracapacitor. Do not try this at home!

Of course, you can always make your own capacitor with paper and electrically conductive paint.

Now download the pdf below. It contains notes to help with your prelim revision and some extra capacitor problems.

Thanks to Fife Science for the original pdf from Martin Cunningham.

beautiful equations

Those of you not out celebrating New Year might have spotted a programme called Beautiful Equations on the BBC schedule.  The programme follows an artist as he asks about five famous physics equations.

One of the featured equations should be familiar to you from unit 1 of the AH Physics course;

F = \displaystyle {{G m_1 m_2} \over r^2}

Hopefully you recognise this as Newton’s equation for the gravitational force between two bodies.  I have extracted the nine minutes or so relating to Newton’s work and embedded it below.

The link below will download the entire programme, which also looks at E=mc^2, time dilation in special relativity, the Dirac equation and Stephen Hawking’s work on black holes.

Wheatstone bridge circuits

We’ve just completed the section of Higher unit 2 that investigates the behaviour of a Wheatstone Bridge. The bridge circuit is really just a pair of voltage dividers connected in parallel.  A voltmeter, ammeter or galvanometer (very sensitive ammeter) connects the two voltage divider chains together, as shown below.

When the voltage (or current) displayed on the meter is zero, we say that the Wheatstone bridge is balanced.  For a balanced bridge, it is possible to show that

\displaystyle {R_1 \over R_2} = \displaystyle {R_3 \over R_4}

[you have this proof in your notes folder]

For the circuit shown above, the voltmeter will display the difference in electrical potential between points B and D.  We can calculate this potential difference by finding the voltages at points B and D using the voltage divider equation you used for Standard Grade/Intermediate 2 Physics.

V_2  = \displaystyle { R_2 \over {R_1+R_2}} \times V_s

So in this example,

V_D = \displaystyle {R_2 \over {R_1+R_2}} \times V_s

and

V_B  = \displaystyle {R_X \over {R_3+R_X}} \times V_s

The voltmeter displays the potential difference between these two points, i.e.

V_G  = V_D-V_B

Here is a short video that provides a recap of the Wheatstone Bridge.

and a worked example from an old SQA past paper

Now click on the picture below to try an interactive Wheatstone Bridge problem (you will need to have Java installed).

Instructions:

  • Press the Reset button to change the value of all the resistors in the circuit.
  • Use the slider to balance the bridge. The circuit uses a centre-zero meter, so aim to get the indicator dead centre.
  • Find the unknown resistance (R4) using the value of the other 3 resistors when the circuit is balanced.

You can repeat this simulation as many times as you like by pressing Reset to change the resistor values…..it’s great practice!

Here is an example of an application of the Wheatstone Bridge, called the metre bridge.

When a Wheatstone Bridge is slightly out of balance, it will provide a linear response.  In other words, small changes in resistance will produce proportionally small changes in voltage or current.  When these small changes are plotted, we obtain a straight line through the origin, like this:

We tried to use this property of a Wheatstone Bridge to find the temperature of the physics classroom.  We used some of the snow outside for a low temperature and boiling water for a high temperature.

As we discussed today, this was not a particularly successful experiment due to the non-linear response of the thermistor to changes in temperature – you might remember this from Standard Grade or Int 2 Physics.

For temperature ranges much smaller than the 100°C we attempted, it is possible to obtain an accurate estimate of room temperature.

Click on the download link below to try some Wheatstone Bridge questions.

x-rays in medicine

X-rays are a form of electromagnetic radiation.  They have a much higher frequency than visible light or ultraviolet.  The diagram below, taken from Wikipedia, shows where x-rays fit into the electromagnetic spectrum.

image by Materialscientist

Wilhelm Röntgen discovered x-rays and the image below is the first x-ray image ever taken.  It shows Mrs. Röntgen’s hand and wedding ring.  The x-ray source used by Röntgen was quite weak, so his wife had to hold her hand still for about 15 minutes to expose the film.  Can you imagine waiting that long nowadays?

This was the first time anyone had seen inside a human body without cutting it open.  Poor Mrs. Röntgen was so alarmed by the sight of the image made by her husband that she cried out “I have seen my death!” Or, since she was in Germany, it might have been “Ich habe meinen Tod gesehen!” that she actually said.

Röntgen continued to work on x-rays until he was able to produce better images. The x-ray below was taken about a year after the first x-ray and you can see the improvements in quality.

Notice that these early x-rays are the opposite of what we would expect to see today. They show dark bones on a lighter background while we are used to seeing white bones on a dark background, such as the x-ray shown below.  The difference is due to the processing the film has received after being exposed to x-rays.

In hospitals, x-rays expose a film which is then developed and viewed with bright light.  X-rays are able to travel through soft body tissue and the film behind receives a large exposure.  The x-rays darken the film. More dense structures such as bone, metal fillings in teeth, artificial hip/knee joints, etc. block the path of x-rays and prevent them from reaching the film.  Unexposed regions of the film remain light in colour.

Röntgen’s x-ray films would have involved additional processing steps.  The exposed films were developed and used to create a positive.  In creating a positive, light areas become dark and dark areas become light.  So the light and dark areas in Röntgen’s x-rays are the opposite of what we see today.  Our modern method makes it easier to detect issues in the bones as they are the lighter areas.

Röntgen was awarded the first ever Nobel Prize for Physics in 1901 for his pioneering work in this field of physics.

Medical imaging has come a long way since Röntgen’s discovery of x-rays.  This promotional video from German company Siemens outlines the advances that have been made since the early 20th century.

I have attached a recording of a short BBC radio programme about the first x-ray and what people in the Victorian era thought of these new images.  Click on the player at the end of this post or listen to it in iTunes.