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- Exact differential – for a very first idea feel free to look up the Wikipedia article. Make sure, however, to consult the literature for relevant examples!
- Measurement error types (random, systematic, etc.) and their sources.
- Basics of using engineering equipment: caliper, micrometer screw, etc.
- Rounding up numbers (applied to measurement results and errors) – consult the script!

- reports – each of them is a partial grade,
- tests – first of them on the introductory material (see Section 1) and possibly more on the actual exercises being done.

- short
*table*containing topic, number and date of the exercise, your name and lastname, group, course of study, faculty, - a short but relevant introduction (not a reprinted script!) – i.e.
**what**has been done in the exercise,**how**and**what for**, some formal background (mathematical description) is also a good idea, - measurement results – what did you get in terms of actual numbers, units, errors,
- any calculations that need to be done – these according to the script – including calculated complex errors (if necessary/relevant),
- summary – what's the final result? If it's a known physical constant – compare with a textbook and make a comment. What are the main sources of errors encountered? Any further thoughts/comments?

**EXERCISE #101**: *Speed of light (PDF file)*

**EXERCISE #102**: *Gravitational acceleration (PDF file)*

**EXERCISE #103**: *Linear expansion of solids (PDF file)*

**EXERCISE #104**: *Moment of inertia (PDF file)*

**EXERCISE #105**: *Young's modulus (PDF file)*

**EXERCISE #106**: *Uniformly accelerated motion (PDF file)*

**EXERCISE #107**: *Viscosity (PDF file)*

**EXERCISE #201**: *Capacitors: studying capacity by means of relaxation oscillations.* Please get familiar with the following: *alternating/direct current (AC/DC)*, *capacitor (working principle, properties, e.g. capacity, etc.) *, *electrical resistance*, *neon light*.

Measurements:

- in order to determine the K constant of the system, measure the time of 10 flashes of the neon light for 15-20 combinations of resistance (R) and reference capacity (C); values of R and C should be applied such that the flashes are easy enough to observe;
- for each of the unknown capacitors and for each of resistors measure the time of 10 flashes.
Report (on top of an introduction according to instructions given at the bottom of the page):

- for every measurement calculate the period (
T) of the flashes;- for every reference capacity measurement, determine the
Kconstant given by relationT=RCK(where T – time period, R – resistance, C – capacity, all of which are known) of the system as well as its mean value and deviation;- by using the K constant, calculate capacities
Cof the unknown capacitors;- calculate the mean value of the capacity for each capacitor and determine its deviation (error);
- formulate conclusions.

**EXERCISE #202**: *Electrical transformers.* Please get familiar with the following: *working principle of an electrical transformer*, *alternating/direct current (AC/DC)*, *power rating*, *ratio* and *efficiency of a transformer*, *load/no-load state*, *open/short circuit*.

Measurements:

No-load state:- set the turns
n1=400andn2=600; the "W" switch goes to off (0 – disconnected);- set the voltage knob to 1 V and turn it on;
- turn the multimeters on in the AC mode;
- keep changing the power voltage by 1 V in the range of 1-10 V, each time recording the voltage
U1andU2;- repeat the measurements for
n1=400andn2=400, 200.

Short-circuit state:- set power voltage to 1 V, the "W" swith to "1" (on) and the resistor to zero;
- measure currents
I1andI2in analogy to the previous measurements (meaning:n1=400andn2=600, 400, 200);- when you're done, set the power voltage to 1 V.

Load state:- set
n1=400,n2=200;- set power voltage to 4 V and the "W" switch to "1";
- do up to 15 measurements of
U1,I1,U2andI2changing the resistance in the range of 0-34 Ohms (by the step of 1, 2 and 4 at the end of range);- set the "W" switch to "0" and record the values of
U1,I1,U2andI2;- set the power voltage to 1 V and turn ot off.
Report (on top of an introduction according to instructions given at the bottom of the page):

- plot (on a single graph) the secondary voltage as a function of primary voltage
U2=f(U1);- determine the ratios of the transformer as well as their mean values and deviations (errors); ratio
K=n1/n2=U1/U2, where: U1, U2 – voltages, n1, n2 – numbers of coil turns;- determine the theoretical ratios of the transformer (ratios of the number of primary/secondary turns) and compare with the measured ones;
- plot (on a single graph) the
I2=f(I1);- plot (on a single graph) the
U2=f(I2);- calculate the efficiencies of the transformer for each measurement and plot them as a function of primary current; efficiency η
=[(U2 I2) / (U1 I1)] 100%;- formulate conclusions.

**EXERCISE #203**: *Electrical conductors and semiconductor: studying conductivity as a function of temperature.* Please get familiar with the following: *conductor/semiconductor*, *temperature (and how it affects matter)*, *electrical resistivity*.

Measurements:

- measure resistance R for both conductor and semiconductor in the temperature range from the room temperature up to 90 ℃.
Report (on top of an introduction according to instructions given at the bottom of the page):

- plot
R=f(T)for both conductor and semiconductor at the same graph for comparison; feel free to use differennt scales if needed;- for a semiconductor: calculate
ln(1/R)and1/Tand plot those functions; temperature need to be expressed in Kelvins;- using linear regression determine the slope coefficient and its error;
- try to determine the energy doping level according to the formula:
a=E/2k, where: E – energy of the doping level, k – Boltzmann constant. The doping level can be calculated approximately; the functionln(1/R)=f(1/T)(see above) is linear and we can use the linear regression to determine the slope coefficienta. Regression can be done by using e.g.gnuplotor an office suite such asLibre Office. Havinga, we can finally calculateEfrom the relationa=E/2k;- try to calculate complex error of E given above (exact differential); you can use a spreadsheet (e.g. MS Excel) to calculate the
standard deviationofaas well;- formulate conclusions.

**EXERCISE #204**: *Electrical conductor within external magnetic field.* Please get familiar with the following: *magnetic field*, *Lorentz force*.

Measurements/report:

- determine the electrodynamic force as a function of electric current flowing through the frame,
FED=f(I);

- gradually increase the current, so that the laser pointer indicates positions with
1 cmsteps; each time record the positions of the laser pointer as well as the current value (I);- repeat the measurements for an increasing number of coil turns (5,10,15,20,25);
- calculate
FED=f(I)for each frame inclination; use the relation:FED=cx, wherecis the frame inclination (measured on a centimeter scale),c=(2.65 +/- 0.05) N/m;- plot the above functions on a single graph;
- determine the electrodynamic force as a function of coil turns,
FED=f(n);

- in the
FED=f(I)plots read the approximate values ofFEDfor a single (constant) current value within the range of 0.15-0.25 A;- for
I=const.plot theFEDas a function of the number of coil turns,FED=f(n);- determine magnetic field induction
Bbetween the magnetic poles,

- choose one of the
FED=f(I)plots – the one closest to a linear plot – and by using the linear regression determine its slope coefficientaR;- calculate the magnetic field induction,
B=aR/na, where:aR– slope coefficient,n– number of coil turns,a=(13.0+/-0.2) cm;- try to calculate the complex error (exact differential).

**EXERCISE #205**: *Determining Planck's constant and work function by means of photoelectric effect.* Please get familiar with the following: *photoelectric effect*, *work function*, *Planck's constant*.

Measurements:

- for a selected filter available on the workstation do the following: set
U1voltage to10 Vand keep gradually lowering it while recording the U2 value until it reaches zero;- cut off the light; set
U1=0and readU2which is theU0;- turn the light on again; set the negative voltage
U1such that the previously measuredU2has the reference valueU0; then theU1is thebreak voltage Uh;- determine the
break voltage Uhfor all the remaining filters; do the standard series of three measurements for each.Report (on top of an introduction according to instructions given at the bottom of the page):

- knowing values of
U2andRcalculate the photocurrent and plot it as a function:I=f(U1);- knowing the wave lenghts of the filters – calculate the frequencies;
- plot the
break voltage Uhas a function of frequency;- by using linear regression: determine the slope coefficient and the point at which the function crosses Y axis;
- calculate Planck's constant (h) and work function (W) and their standard deviations;
- formulate conslucions.

**EXERCISE #206**: *Ferromagnets, hysteresis loop and Hall effect.* Please get familiar with the following: *Ferromagnetism/paramagnetism/diamagnetism*, *Curie temperature*, *hysteresis loop*, *Hall effect*.

Measurements:

- while changing the current
I, record the corresponding Hall voltageVhaccording go the following procedure;- increase the current gradually (step of 0.2 A) up to ~3 A (not to exceed 3 A);
- decrease the current gradually to zero;
- switch the direction of current;
- repeat the measurements up to ~3 A and down to zero again;
- switch the direction of current and finish up the measurements reaching 3 A value once again.
Report (on top of an introduction according to instructions given at the bottom of the page):

- determine the magnetic field
H=n*I(n =6, i.e. number of coil turns; I – current) and the inductionBknowing thatVh=γ*iH*B(γ=(140 ± 5) V/AT; iH=(10,0 ± 0,5) mA, Vh – measured Hall voltage);- plot
B=f(H);- determine ΔB and ΔH;
- formulate conclusions.

**EXERCISE #207**: *Thermocouples.* Please get familiar with the following: *thermocouples*, *Seebeck effect*, *Thomson effect*, *Peltier effect*, *Fermi level*, *work function*.

Measurements:

- measure the thermoelectric voltage on each thermocouple (A-C) as a function of temperature – according to the instructions given in class.
Report (on top of an introduction according to instructions given at the bottom of the page):

- plot the thermoelectric voltage as a function of temperature (
U=f(T)) for each thermocouple;- as for the linear part – use the linear regression to determine thermoelectric coefficient α;
- determine the deviation of α for each temperature and express the final results according to the rules (rounding numbers, proper units, etc.);
- formulate conclusions.

**EXERCISE #301**: *Determining refractive index by means of real and apparent thickness measurement.*

Measurements:

- use the computer and
MOCAPsoftware; turn the microscope light on;- do the measurements according to the instructions given in class.
Report (on top of an introduction according to instructions given at the bottom of the page):

- plot the thermoelectric voltage as a function of temperature (
U=f(T)) for each thermocouple;- as for the linear part – use the linear regression to determine thermoelectric coefficient α;
- formulate conclusions.

**EXERCISE #302**: *Determining focal lenght.*

Measurements:

- place selected lense in the holder;
- note position of the light source and screen;
- find two positions of the lense for which the image is sharp – record these (
x1,x2;- change the screen position and find the sharp images again;
- repeat the measurements for all focusing lenses and combinations of focusing and difusing lenses.
Report (on top of an introduction according to instructions given at the bottom of the page):

- determine distances: object-lense and screen-lense;
- find the focal lenghts according to the equation:
1/f=1/x+1/yand determine the deviations;- to use the Bessel method:
- determine distances: object-screen and between
x1andx2;- determine focal lenghts (focusing lenses) by using the Bessel equation:
f=(l^2-e^2)/4l;- determine focal lenghts (combinations of lenses) by using the equation:
1/f=1/f1+1/f2-d/(f1f2)

**EXERCISE #303**: *Determining grating constant.*

Measurements and report:

- find the light source image in tht object-glass – note the position on the scale (
V0);- find all bands on the left/right from the zero-order image for all given diffraction gratings;
- determine grating constant for each system:
d=mλ/sin(V), wheremis the order of observed image,Vis the angle relative to the zero-order image;- calculate the mean value and standard deviation;
- formulate final results.

**EXERCISE #304**: *Optical emission spectra.*

Measurements and report:

**EXERCISE #305**: *Refractive index and Abbe refractometer.*

Measurements:

- prepare the setup (according to the in-class instructions);
- place the selected sample (a thin film of liquid) in the space between the prisms;
- turn the two refractometer knobs in order to observe the sharp boundary (line) between the dark and light areas in the middle of the view window;
- read the refractive index
nfrom the scale below the view window;- repeat the measurements for all the samples (different concentrations) including the unknown sample (concentration
X);- make sure to clean the prisms before placing the sample;
- in addition: for the 100% concentration (glycerol) measure the refractive index as a function of temperature (
T).Report:

- plot the refractive index as a function of concentration;
- plot
n=f(T);- if necessary, make use of the linear regression and try to determine the
Xconcentration of glycerol.

**EXERCISE #306**: *Polarisation of light.*

Measurements:

- lenght of the sample containers
L=(0.185±0.005) m;- set the object-glass to be able to see sharp lines separating areas of different shading;
- place the clean water sample within the polarimeter and turn the analyser to see equal (homogeneous) shading of the view window; measure the corresponding angle (repeat the measurement at least three times);
- repeat the procedure for all the samples including the one with unknown concentration (marked
X), i.e. keep measuring the angle corresponding to given concentration.Report:

- determine polarisation angles (
α) for each concentration;- plot
α=f(c);- use linear regression to find slope coefficient and its deviation;
- determine the proper ability of twisting the polarisation (and its deviation) given by:
[α]=a/l, where a – slope coefficient, l – length of the sample container;- find the concentration of the
Xsample;- summarize the results and conclusions.

**EXERCISE #307**: *Efficiency of light sources.*

Measurements and report:

Copyright (c) 2017, 2018 M. Hermanowicz