Measure the uncertainity in the derived quantity

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The Cathode Ray Oscilloscope

Introduction 

The following should give the student some familiarisation with the function and uses of the cathode ray oscilloscope (C.R.O.).

Consider a simple sine wave electrical signal from some source as in Fig. 1a. If we can arrange things so that this sinusoidal voltage is applied to two horizontal conducting plates then in the region between these plates, the electric field will be alternating with period T seconds. It will increase in strength to a maximum, decrease to zero, turn over, and increase in the opposite direction to an equal maximum, then decrease to zero again, in each period of time T.

Now, if there is a beam of charged particles (electrons) streaming between these horizontal plates, the oscillating electric field there will bend the beam first up, then down, then back to the undeflected position in each time period T. Further, if the beam strikes a plate of material which fluoresces, one would see a spot of light on this plate (screen) which moves vertically up and down with period T.

 Now consider a set of vertical plates, also straddling the electron beam. An electric field applied to these plates will deflect the beam horizontally by an amount proportional to the voltage applied across the plates. If, connected to these plates we have a circuit which generates a linear ramp voltage, periodically, with the same period T, as in Fig. 1b, then the spot on the screen would be forced to start at the left side and move linearly in time across the screen, reaching its maximum travel to the right at time T. The spot would disappear then, and instantaneously reappear back where it started at the left hand side. This “sweep” would repeat every time T. You may wonder how one can easily produce a sawtooth wave at exactly the frequency of the input signal (or if you don’t, you should!). The answer is simple; you use the input signal to trigger the ramp (ie. to start it at its lowest voltage) every time the input voltage reaches a particular value going in a particular direction (ie. increasing or decreasing). In this way, if the input is periodic, then the sawtooth will have the same period, by definition.


The first set of plates, driven with the sinusoidally varying voltages will produce on the screen a spot travelling up and down in simple harmonic motion. If fast enough, it will appear as a solid vertical line. (Figure 2a) The second set of plates, driven with the ramp signal, if fast enough, produces a horizontal line on the screen, as in Figure 2b.

A combination of both sets of plates, one with a sinusoidal driving voltage of period T, the other with a ramp period of period T, will produce on the screen a picture like Figure 2c, (if the two circuits are synchronised so that they start as drawn on the voltage vs. time graphs).

 If the ramp period is now doubled, so that the spot sweeps across the screen in a time 2/T, on the sweep left to right the sinusoidal voltage will complete two full cycles and the picture on the screen will look like Figure 2d. Hopefully, this introduction will have presented an idea of how the C.R.O. functions in displaying a.c. (ie. time-varying) signals on the screen.

The C.R.O. in Detail 

The main part of the C.R.O. is a highly evacuated glass tube housing parts which generates a beam of electrons, accelerates them, shapes them into a narrow beam, and provides external connections to the sets of plates described above for changing the direction of the beam. The main elements of the C.R.O. tube are shown in Figure 3.

1. K, an indirectly heated cathode which provides a source of electrons for the beam by “boiling” them out of the cathode.
2. P, the anode (or plate) which is circular with a small central hole. The potential of P creates an electric field which accelerates the electrons, some of which emerge from the hole as a fine beam. This beam lies along the central axis of the tube.
3. G, the grid. Controlling the potential of the grid controls the number of electrons for the beam, and hence the intensity of the spot on the screen where the beam hits.
4. F, the focusing cylinder. This aids in concentrating the electron beam into a thin straight line much as a lens operates in optics.
5. X, Y, deflection plate pairs. The X plates are used for deflecting the beam left to right (the x direction) by means of the “ramp” voltage. The Y plates are used for deflection of the beam in the vertical direction. Voltages on the X and Y sets of plates determine where the beam will strike the screen and cause a spot of light.
6. S, the screen. This is coated on the inside with a material which fluoresces with green light (usually) where the electrons are striking.

Does water swirl counter-clockwise in the Southern Hemisphere?

Answer:Yes and no. When applied to toilets and sinks, this is one of those “too good to be true” science factoids, I’m afraid. But it does apply in some situations.

The myth goes that if you flush a toilet in Australia the water swirls down the drain the opposite way than in the northern hemisphere, due the Coriolis effect (an apparent force which describes how objects veer to the left or right when traveling on something that’s rotating — see the link above for a good visualization of this).

If there were no other forces on that water in the sink or toilet, that would be true. The Coriolis effect does actually make hurricanes rotate the opposite direction in the two hemispheres. But for toilets and sinks it’s another story. The toilet myth is easy to dispell — just peek around the rim of the toilet and you’ll see that the water is jetted into the bowl at an angle, which determines the direction the water swirls. Sinks, however, are a little more tricky.

I’ve heard of charlatans who hang around the equator in Kenya, carrying basins of water. They’ll stand on the southern side of the equator with the basin, pull a plug at the bottom, and show that it swirls out counter-clockwise. Then they’ll walk to the northern side of the equator, fill the basin and pull the plug, and it swirls out clockwise. Irrefutable proof? Be careful! You have to know all the initial conditions in any experiment, and in this one, there is one that is hidden from you. The huckster just has to add a slight rotation to the water before letting it out (for example, pour the water in at a very slight angle to give it an initial rotation, and it will “remember” that rotation as it swirls out of the basin. In fact, you can swirl the water in the basin, then walk away from it for several hours, and it will still “remember” that rotation when you pull the plug! Plus, the charlatans got it backwards — water should actually swirl counter-clockwise in the northern hemisphere if the Coriolis effect were at play! (See Alistair Fraser’s website for a great explanation of how you can re-create this fakery for a fun party trick!)

Even if you don’t give the water an initial swirl, tiny pits and imperfections in the basin can give the water a rotation — which may be clockwise or counterclockwise, but doesn’t depend on which hemisphere you’re in!

Transformer and Hysteresis

Transformer Hysteresis Losses are caused because of the friction of the molecules against the flow of the magnetic lines of force required to magnetise the core, which are constantly changing in value and direction first in one direction and then the other due to the influence of the sinusoidal supply voltage.

This molecular friction causes heat to be developed which represents an energy loss to the transformer. Excessive heat loss can overtime shorten the life of the insulating materials used in the manufacture of the windings and structures. Therefore, cooling of a transformer is important.

Also, transformers are designed to operate at a particular supply frequency. Lowering the frequency of the supply will result in increased hysteresis and higher temperature in the iron core. So reducing the supply frequency from 60 Hertz to 50 Hertz will raise the amount of hysteresis present, decreased the VA capacity of the transformer.

Frogs Levitate in Strong Magnetic Field

Some things like iron nails are known for their magnetic properties, but why should frogs levitate in a magnetic field? The trick is to get the magnetic field right – you can’t just use any old bar magnet to make a frog levitate.

Frogs, like everything around and inside us, are made up of millions and billions of atoms. Each of these atoms contains electrons that whizz around a central nucleus, but when atoms are in a magnetic field, the electrons shift their orbits slightly. These shifts give the atoms their own magnetic field so when a frog is put in a very strong magnetic field, it is essentially made up of lots of tiny magnets. And there’s nothing special about frogs. All materials – including strawberries, water and gold – are ‘diamagnetic’ to some extent, but some are more convenient to levitate than others.

Frogs are convenient not only because they have a high water content, which is a good diamagnetic material, but also because they fit easily inside a tube-shaped Bitter electromagnet. Bitter electromagnets use a very large electric current to create an extremely strong magnetic field which magnetises the frog in such a way that its magnetisation is in the opposite direction to the applied field. This means that the magnetised frog is pushed up from a region of high magnetic field into one of lower field, and levitates.

Have you ever been on a train going through a tunnel or a plane and your ears pop? Why does this happen?

A: Inside your ear there is a pocket of air. This pocket is normally at the same pressure as the air outside your ear to help you hear, but if the air pressure around you changes, you feel the air pushing on your eardrum. Your ear has a small tube for equalising the pressure between the inside and outside of the ear that is opened when you swallow and when the pressure is equalised you often feel a pop.

In a plane, the high altitude means the air is thinner and although planes are pressurised, the air pressure is still much less than on the surface. This difference in air pressure can be felt by the ears, particularly on takeoff and landing when changes in altitude make the pressure difference happen more quickly.

The train in a tunnel is slightly different. When the train enters the tunnel it squeezes the air in front of the train creating high pressure in the cabin and you sense this change in pressure.

There are some ways to equalise the pressure between the inside and outside of the ear. One common way that divers use is to gently try and blow through your nose while you hold your mouth and nose shut.

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