Experiment 8:The voltmeter as an ohmic resistor in a circuit
Apparatus:
AC/DC power supply PRO 0...12 V/3 A, Plug-in board safety socket,20/10, Resistor
4.7 kOhm, STE 2/19, Resistor, 680 kΩ, STE 2/19
Resistor, 220 kΩ, STE 2/19, Multimeter LDanalog 10 , Safety connecting lead 50 cm,
red, Safety connecting lead 50 cm, blue
Procedure:
1. Set up the circuit shown. In the course of the experiment, restrict the time for
which the current flows to a minimum.
2. Explain to students that we expect a coulomb to make the same energy
transfer in every cell. Then we use the effective number of cells as a measure
of the energy transferred to each coulomb.
3. Explain that all the cells will remain in the circuit, to maintain constant
resistance.
4. Record the ammeter reading with all 7 cells facing the same way.
5. Reverse one cell, and read the ammeter for what is now a 5-cell transfer.
6. Continue to reverse one more cell at a time until all 7 are reversed.
7. Plot a graph, which serves as an introduction to Ohm's law.
Diagram:
Theory:
The purposes of this experiment are to test Ohm's Law, to study resistors in series and
parallel, and to learn the correct use of ammeters and voltmeters.
Ohm discovered that the ratio of voltage to current in a metallic resistor is constant as
long as the temperature is held constant. This ratio is called resistance. For small
temperature variations the resistance can be considered essentially constant. Ohm's
Law
is usually written
V = IR
in which V is the potential difference across the resistor (often called simply voltage
across the resistor), in volts. I is the current in amperes and R is the resistance in ohms.
According to Ohm’s Law, if we plot a graph of the voltage across a resistor vs. the
current flowing through the resistor, we should obtain a straight line through the
origin.
The slope of this line is the resistance. When two or more resistors are connected in
series, the equivalent resistance is given by
Req = R1 + R2 + R3 + …..
When two or more resistors are connected in parallel, the equivalent resistance is
given
by
In order for an ammeter to measure the current flowing through a resistor, the
ammeter must be connected in series with the resistor so that the same current flows
through both. An ideal ammeter has zero resistance, so that the current flowing in
each branch of a circuit is unaffected by its presence. A real ammeter has a very small
resistance so that the effect of its presence in the circuit can be neglected. A small
resistance means small compared to the other resistances in the circuit. Similar to real
strings used in Physics 250 which were considered to have small masses.
Because an ammeter has a very small resistance, it must never be connected directly
across a voltage source, because a large current will flow through it and burn it out.
In order for a voltmeter to measure the potential difference across a resistor, the
voltmeter must be connected in parallel with the resistor. An ideal voltmeter has
infinite resistance so that no current flows through it and therefore it does not affect
the rest of260 7-2 the circuit. A real voltmeter has a very high resistance so that the
small current which flows through it can usually be neglected without serious error.
Because a voltmeter has a high resistance, it is protected from burnout, unless it is
connected to a source of voltage substantially higher than its range.
Formula:
Mathematically, this current-voltage relationship is written as,
V=IR
Experiment 09: RLC circuit with Cobra3 and the FG
module
Apparatus:
Cobra3 Basic Unit 12150.00, Power supply, 12 V- 12151.99, RS 232 data cable
14602.00, Cobra3 Power Graph software 14525.61,Cobra3 Universal writer software
14504.61, Cobra3 Function generator module 12111.00, Coil, 3600 turns 06516.01,
Connection box 06030.23, PEK carbon resistor 1 W 5% 100 Ω 39104.63, PEK carbon
resistor 1 W 5% 220 Ω 39104.64, PEK carbon resistor 1 W 5% 470 Ω 39104.15, PEK
capacitor/case 2/1 μF/ 250 V 39113.01,PEK capacitor/case 1/2.2 μF/ 250 V 39113.02
PEK capacitor/case 1/4.7 μF/ 250 V 39113.03, Connecting plug 39170.00 2,
Connecting cord, l = 250 mm, red 07360.01, Connecting cord, l = 250 mm, blue,
Connecting cord, l = 500 mm, red 07361.01, Connecting cord, l = 500 mm, blue
07361.04,PC, Windows ® 95 or higher
Procedure:
The experimental set up is as shown in Figs. 1, 2a and 2b.
Connect the COBRA3 Basic Unit to the computer port COM1, COM2 or to USB
port (for USB computer port use USB to RS232 Converter 14602.10).
Start the "measure" program and select "Gauge" > "Cobra3 Power Graph".
Click the "Analog In2/S2" and select the "Module /Sensor" "Burst measurement" with
the parameters seen in Fig. 3.
Click the "Function Generator" symbol and set the para- meters as in Fig. 4.
Add a "Virtual device" by clicking the white triangle in the upper left of the "Power
Graph" window or by right-clicking the "Cobra3 Basic-Unit" symbol. Turn off all
channels but the first and configure this one as seen in Fig. 5
Figure:
The "Settings" chart of PowerGraph should look like Fig. 6.
Configure a diagram to be seen during the measurement on the "Displays" chart of
PowerGraph as in Fig. 7 and turn on some Displays for the frequency, the voltages
and the current
Set up a series tuned circuit as seen in Fig. 2a. Start a measurement with the
"Continue" button. After the measurement has stopped, the recorded curves are
visible in the "measure" program main menu.
Record curves for RD = 0 Ω, 220 Ω, 470 Ω with the 2.2 μF capacitor.
– Record curves for RD = 0 Ω with the 1 μF capacitor and the 4.7 μF capacitor.
– Use "Measurement" > "Assume channel..." and "Measurement" > "Channel
manager..." to display the threeimpedance curves with the damping resistor values
RD = 0 Ω, 220 Ω, 470 Ω for the 2.2 μF capacitor in a single plot. Scale the impedance
curves to the same value either using the "Scale curves" tool with the option "set to
values" or using "Measurement" > "Display options..." filling appropriate values into
the field "Displayed area" on the "Channels" chart. The result may look like Fig. 8.
– In a similar way produce a plot of the impedance over the frequency for the series
tuned circuit with no additional damping resistor and the three capacitance values C =
1 μF, 2.2 μF, 4.7 μF. Fig. 9 shows a possible result.
Note which of the curves, current or voltage, was ahead of the other.
– Use "Analysis" > "Smooth..." with the options "left axis" and "add new" on both
current and voltage curves. The curve that was clicked on before will be processed.
– Use "Measurement" > "Channel manager..." to select the "Current FG' "values as xaxis and the "Analog in 2' "-voltage values as y-axis (Fig. 13). The Lissajous-figure to
be produced now is no function but a relation so select in the "Convert relation to
function" window the option "Keep measurement in relation mode".
– Use the "Survey" tool to determine the maximal extension of the Lissajous-figure in
x-direction ∆Imax (Fig. 14) and the extension of the figure on the y = 0 line ∆I0 (Fig.
15).
– The ratio ∆I0 / ∆Imax equals the sine of the phase shift angle sin(w) between
current and voltage.
– Calculate w and tan( w) for the used frequencies and plot them over the frequency
using "Measurement" > "Enter data manually..." (Fig. 16).
– You may use "Measurement" > "Function generator..." to compare calculated
theoretical values with the measured values. Fig. 17 shows the equation for coil with
L =0.3 mH and d.c. resistance RL = 150 Ω in series with a 2.2 μF capacitor with no
additional damping resistor.
Theory:
Series tuned circuit
A coil with inductance L and ohmic resistance RL , a capacitance C and an ohmic
resistance RD are connected in series to an alternating voltage source
U1t 2 Uˆ · e ivt
with the angular frequency v = 2 p f . The ohmic resistances add up to a total ohmic
resistance R = RL + RD . Inductance L and ohmic resistance RL of the coil are in
series because all the current going through the coil is affected by the ohmic
resistance of the long coil wire. Though Lenz's rule states UL = - L · dI/dt, here the
polarity of the voltage on the coil has to be included as positive, because if a voltage
is switched on on an ideal coil, the induced voltage on the coil is such, that the
positive pole of the coil is there, where it is connected to the positive pole of the
voltage source.
Experiment 10: Kirchhoff’s laws with Cobra4
Apparatus:
1 Power supply, 0..12 V, 0..5 A, 1 Cobra4 Wireless Manager, 1 Cobra4 Wireless-Link,
1 Cobra4 Sensor-Unit Energy, current, voltage, power, energy, esistor 1 W 100 Ω,
resistor 1 W 220 Ω , resistor 1 W 330 Ω, resistor 1 W 470 Ω , resistor 1 W 1.0 kΩ ,
resistor 1 W 2.2 kΩ, 1 resistor 1 W 3.3 kΩ, 1 resistor 1 W 4.7 kΩ, 1 resistor 1
W 10.0 kΩ, 1 connection box, 3 connecting plug, 2 connecting cord, red, 250 mm, 2
connectiong cord, blue, 250 mm, 2 connecting cord, black, 100 mm, 1 software
cobra4 - multi user licence, Additional required 1 PC, windows XP or lighter
Procedure:
plug the connection cords into the correct sockets of the Cobra4 Sensor-Unit Energy.
Before switching on the power supply, make sure that both adjustments of current and
voltage are tuned down to zero. After switching on the power supply first tune the
current until the red LED goes out. Then carefully tune up the voltage to a maximum
of 1 V. If the red LED lights up again you have to adjust the current. Keep an eye on
the Cobra4 Sensor-Unit Energy measuring the current in the circuit and keep the
current well below 1 A. In order to determine the unknown resistance change R2 until
the current through U5/I5 vanishes. You may try single resistors as well several
resistors connected in series to vary R3. Note down the combinations at which the
current becomes zero or at least reaches a minimum.
Theory:
Task 1
With branched circuits, in the steady-state condition, Kirchhoff’s 1st law applies at
every junction point
Σk Ik = 0
Where Ik are the currents leading to or from the junction point. This means, that in
every junction point, the charge is conserved. It is customary to take Ik as negative if
the corresponding current in the k-th conductor is flowing away from the junction
point. For every closed loop C in a network of linear conductors, in the steady-state
condition, Kirchhoff’s 2nd law applies:
Σk Uk = 0
Where Uk the voltage in the k-th conductor. This is a special case of the induction law
as it applies only for constant magnetic flows. More precisely, it is a conclusion of the
1st and 3rd of Maxwell’s equations. It means that, in a closed loop, the electrical
energy is conserved.
Result:
Experiment 11: Ferromagnetic hysteresis with Cobra4
Apparatus:
Coil, 600 turns 2, Iron core, U-shaped, solid, Iron core,solid, Iron core, U-shaped,
laminated electric steel, iron core, short, laminated, commutator switch, PHYWE
power supply, universal, analogue display DC: 18 V, 5 A / AC: 15 V, 5 A, Hall probe,
tangential, protection cap, Barrel base PHYWE, Right angle clamp expert, Support
rod, stainless steel, I = 250mm, d = 10 mm, Cobra4 wireless/USB link incl. USB
cable, Cobra4 sensor-unit electricity, current ± 6A / voltage ± 30V. Cobra4 sensor
tesla, USB charger for Cobra4 mobile link 2 and wireless/USB link, Connecting cord,
32 A, 250 mm, red, Connecting cord, 32 A, 250 mm, blue, Connecting cord, 32 A,
500 mm, red, Connecting cord, 32 A, 500 mm, blue, Software Cobra4 - multi-user
licence, Universal clamp.
Procedure:
The experimental set-up is shown in Fig. 1. Place the solid coil set-up far from the
computer and from the Cobra device to avoid influences of the magnetic fields on the
equipment and sensors. Put the Sensor-Unit Tesla on the first Wireless/USB-Link, the
Sensor-Unit Electricity to the second one. Connect both Wireless/USB-Links with the
computer. Connect the cable of the Hall probe with the Sensor-Unit Tesla and attach
the Hall probe under the top iron bar in such a manner that the sensor is located
close to one of the bars sticking in the coil. The flux density B0, measured by the hall
probe, and the current I through the coils are recorded. Open measure LAB and click
on "PHYWE experiments". Then load the experiment so that all necessary settings
can be loaded. Check that the recording rate is set to maximum 5 Hz. For the
hysteresis measurement the current I, the magnetic flux density B are measured. The
magnetic field density H is calculated and measured with a virtual channel (H =
2459.I) Remember: Do not change the switch's position while a voltage is applied and
do not turn off the voltage rapidly. Otherwise induced current/voltage may damage
the setup. If residual magnetism is present in the iron core, it is demagnetized: Set the
commutator switch in such a manner that an opposing field is generated. Slightly
increase the voltage till the flux density changes sign. Repeat that till the flux density
is approximately zero. Please remember that the Hall-Sensor might have an offset.
You can check if there is residual magnetization by lifting the top iron bar. Set the
current limiter of the power supply to 5 A. After pressing the icon , slowly and
steadily increase the voltage from zero upwards and decrease it to zero again. Using
the commutator switch reverse the polarity of the voltage. Again increase and then
decrease the voltage in the same way. Once again reverse the polarity of the voltage
with the commutator switch and increase the voltage. Click on the icon in the icon
strip to end measurement and reset the voltage to 0 V. An example for the collected
flux-density curve is shown in fig.2. All collected data can get accessed at the "Data
pool". Check wether the virtual channel for the magnetic field strength H (H = 2459.I)
is saved as well. To evaluate the data, plot the magnetic flux density B against the
field strength H to obtain curves shown in fig. 3, 4 and 5. Then repeat the experiment
with the laminated coil set.
Remarks:
To protect the sensor, the flux density should not exceed 1000 mT.
Theory:
The field strength is calculated with the formula
H = I. n/L
where H represents the magnetic field strength,
n = number of turns in the coil (600 turns),
and L = average field line length in the core.
(solid core: Lsc = 232 mm laminated core: Llc = 244 mm)
The factor n/L changes due to the different dimensions of the two iron cores as
follows:
Solid iron core: n/L = 2586 in 1/m
Laminated iron core: = 2459 in 1/m
The calculation of the field strength is combined with a change of the x-axis in the
visualisation.
The factor in the mathematical ”Operation” depends on the used iron core and is equal
to n/L.
Now, the coercive field strength and the remanence can be extracted from the
hysteresis. Therefore, use the ”zoom” function in
the region of the intersection of the axes and then choose ”survey” to obtain the points
of intersection of the x and y-axis with
aid of the cursor lines, which can be freely moved and shifted. A comparison of fig. 3
and 4 shows that the remanence and
coercive field strength are sub-stantially greater in a solid iron core than in a
laminated one.
Typical values for this experimental set-up are:
iron core:
coercive field strength:
remanence:
massive
436 A/m
143 mT
laminated
80 A/m
41 mT
Experiment 12: Dielectric Constant of different materials
Apparatus:
Set of parallel plate capacitors (Diameter = 26 cm), High voltage power supply (010kV), A 10 MΩ resistor, Reference capacitor (220nF), Universal measuring
amplifier, Voltmeter, Dielectric materials (Plastic and glass plates), Connecting cables,
adapters, T-connectors.
Procedure:
1. To start with, the surface area of the capacitor plates is determined using their
given radius.
2. For this experiment, we will be needing 0-5kV from the power supply. So select
the range of the power supply accordingly. The middle terminal will act as “0” for
0 – 5kV range. Please switch off the supply when not in use and be extremely
careful while handling this high voltage source.
3. For charging the capacitor plates, connect the highly insulated capacitor plate
connected to the positive terminal of the high voltage power supply through the
10 MΩ protective resistor. The other plate is connected to the middle terminal of
the power supply and grounded (see Fig. 1).
Fig. 3: Experimental set up and its schematic4. Similarly, for discharging the plate
capacitor, remove the high voltage probe and
switch off the power supply. Connect the BNC cable to the insulated plate. The
other end of the BNC is connected to the 220nF through a T-connector.
5. The voltage appearing across 220nF is fed to the amplifier and the output of the
amplifier is read out on a voltmeter. The amplifier should be set to: i) high input
resistance, ii) amplification factor at 1 and iii) time constant at 0.
6. Be sure not to be near the capacitor during measurements, as otherwise the
electric field of the capacitor might be distorted.
7. You may need to use a drier to get rid of moisture from the plate surfaces if
the humidity is very high. Do this when your data becomes irreproducible.
A. Measurement of charge Q for different supply voltage UC with air as a dielectric
medium:
1. Set the air gap between the two plates to be around 2 mm using the vernier
attached to the capacitor plate.
2. Check that output voltage on voltmeter is 0 by doing “zero adjustment” (to be
done once just at the beginning of the experiment) and then using “reset to zero”
button (to ensure the Cref is completely discharged) before taking every
measurement.
3. Set the voltage on the power supply, UC, at 0.5kV.
4. Charge the capacitor plate as mentioned in step 2 of previous section. Once
charged completely, remove the high voltage probe and switch off the power
supply.
5. Now to transfer the charge on plate capacitor to Cref follow steps 3 and 4 of the
previous section. Note down the maximum voltage reading on the voltmeter, V0.
6. Vary the voltage from 0.5kV to 4kV in steps of 0.5kV and note down
corresponding values of V0. Calculate Q in each case.
7. Plot a graph of Q ~ UC and fit it with a straight line. Determine Er for air.
B. Measurement of charge Q for different distances d:
1. Arrange the set up with an air gap of 1mm (set the gap using the scales on the rail)
and UC = 1.5 kV (say).
2. Follow steps 2-4 of part A and determine Q.
3. Vary the distance from 1 – 4mm in steps of 0.5 mm using the vernier attached to
the plate capacitor. Measure Q.
4. Plot Q ~ 1/d. Check if it fits with a straight line.C. Measurement of charge Q for
different supply voltage UC with a dielectric
(plastic/glass):
1. Place the dielectric (plastic/glass) sheet between the capacitor plates and make
sure that the surfaces of plates touch the sheet completely without any air gap.
Secure the sheet using the vernier attached to the plate capacitor. Be extremely
careful while placing and securing the dielectric between the capacitor plates.
2. Vary UC between 0.5 – 4 kV in steps of 0.5kV. Note the value of V0 in each case
using the same procedure described above and determine Q.
3. Plot Q ~ UC. Determine capacitance and the dielectric constant of
glass/polystyrene.
Observations:
Table-1: Q ~ UC Cref= 220 nf , d (air) = 2 mm
UC (kV)
A=.......
V0 (V)
Q (in nAs) = Vo.Cref
0.5
--
--
Table-2: Q ~ 1/d
A=...., Cref = 220nF, Uc = ... kV
d (mm)
1
---
V0 (kV)
Q (in nAs) = Vo.Cref
Table 3: Q ~ UC (with dielectrics) A=..., Cref = 220nF
UC (kV)
Plastic
V0 (V)
Q = Vo.Cref
nA/s
V0 (V)
Glass
Q = Vo.Cref
nA/s
0.5
--Typical values of Er for air: 1.0006
Plastic ~ 3.
Glass ~ 3.8 – 14.5
Circuit Diagram:
Theory:
Electrostatic processes in vacuum are described by the following integral form of
Maxwell’s equations:
where E is the electric field intensity, Q the charge enclosed by the closed surface A,
E
0
is the permittivity of free space and s a closed path. If a voltage Uc is applied between
two capacitor plates, an electric field E (Fig. 1) will prevail between the plates, which
is
defined by:
Due to the electric field, equal amount of electrostatic charges with opposite sign are
drawn towards the surfaces of the capacitor. Assuming the field lines of the electric
field
always to be perpendicular to the capacitor surface, for small distances d between the
capacitor plates, Eq. 1 and 3 give
The charge Q on the capacitor is thus proportional to voltage the
proportionality constant C is called the capacitance of the plate
capacitor.
The linear relation between charge Q and voltage Uc applied to the
otherwise unchanged capacitor is represented in fig. 4. Eq. 5 further
shows that the capacitance C of the capacitor is inversely proportional
to the distance d between the plates and directly proportional to the
area A of the plates:
Fig. 1: Electric field lines
between capacitor plates
Equations (4), (5) and (6) are valid only approximately, due to the assumption that
field lines are parallel. With increasing distances between the capacitor plates,
capacitance increases, which in turn systematically yields a too large electric constant
from equation (6). This is why the value of dielectric constant should be determined
for a small and constant distance between the plates (Fig. 1).
Once an insulating material (dielectrics) is inserted between the plates the above
equations are modified. Dielectrics have no free moving charge carriers, as metals
have, but they do have positive nuclei and negative electrons. These may be arranged
along the lines of an applied electric field E0. Formerly non-polar molecules get
polarized and thus behave as locally stationary dipoles. As can be seen in Fig. 2, the
effects of the single dipoles cancel each other macroscopically inside the dielectric.
However, no partners with opposite charges are present on the surfaces; these thus
have a stationary charge, called a free charge. The free charges in turn weaken the
effective electric field E as given below.
Experiment 13: Hall effect in metals
Apparatus:
Hall effect, Cu, carrier board, Hall effect, zinc, carrier board, Coil, 300 turns, Iron
core, U-shaped, laminated, Pole pieces, plane, 303048 mm, 2, Power supply 0-30
VDC/20 A, stabil, Power supply, universal, Universal measuring amplifier,
Teslameter, digital, Hall probe, tangent., prot. Cap, Digital multimeter, Meter, 10/30
mV, 200 °C, Universal clamp with join, Tripod base -PASS-, Support rod -PASS-,
square, l = 250 m, Right angle clamp -PASS-, Connecting cord, l = 750 mm, red,
Connecting cord, l = 750 mm, blue, Connecting cord, l = 750 mm, black
Procedure:
The layout follows Fig. 1 and the wiring diagram in Fig. 2.
Arrange the field of measurement on the plate midway between the pole pieces.
Carefully place Hall probe in the centre of the magnetic field.
The measuring amplifier takes about 15 min. to settle down free from drift and should
therefore be switched on
correspondingly earlier.
To keep interfering fields at a minimal level, make the connecting cords to the
amplifier input as short as possible.
Take the transverse current I for the Hall probe from the powersupply unit 13536.93.
It can be up to 15 A for short periods.
The Hall probe will show a voltage at the Hall contacts even in the absence of a
magnetic field, because these contacts are never exactly one above the other but only
within manufacturing tolerances. Before measurements are made, this voltage must
be compensated with the aid of the potentiometer as follows:
Disconnect the transverse current I.
Set the measuring amplifier to an output voltage of 1 V, for example, by adjusting the
compensation-voltage. (he = 104 Ω,
amplification = 105).
Connect the transverse current.
Twist the connecting cords between hall voltage sockets and amplifier input in order
to avoid as much as possible stray
voltages..
Adjust the compensating potentiometer, using a screwdriver, until the instrument
again shows an output voltage of 1 V.
Repeat this operation several times to obtain a precise adjustment.
The determination of the Hall voltage is not quite simple since voltages in the
microvolt range are concerned where the Hall
voltages are superposed by parasitic voltages such as thermal voltages, induction
voltages due to stray fields, etc. The following
procedure is recommended:
Set the transverse current * to the desired value.
Set the field strength B to the desired value (on the power supply, universal,
13500.93).
Set the output voltage of the measuring amplifier to about 1.5 V by adjusting the
compensation-voltage.
Using the mains switch on the power supply unit, switch the magnetic field on and off
and read the Hall voltages at each
on and off position of the switch (after the measuring amplifier and the multi-range
meter have recovered from their peak
values). The difference between the two values of the voltage, divided by the gain
factor 105, is the Hall voltage UH to be
determined.
Figure:
Theory: