TP Physique 2
Aperçu des sections
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List of physical electrical quantities
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Use of Electrical Equipment
Use of the Ammeter
The ammeter is an electrical device used to measure the intensity of an electric current circulating in an electrical circuit. It is designated in a circuit by the symbol
An ammeter must always be placed in series in an electrical circuit because of its small internal resistance. On an ammeter, we notice values mentioned having different units (A, mA…), these represent what we call a caliber.
Realize the electrical circuit of the figure 1, where R represents an electrical resistance and E being the symbol of the direct voltage generator which powers the electrical circuit. Set E to the value E=6V and using a needle ammeter (un amperemètre à aiguilles), measure the intensity of the electric current flowing in the circuit. Report the obtained value without forgetting the unit I =………………………….
Use of the voltmeter
The voltmeter is an electrical device that allows you to measure the voltage at the terminals of an electrical device. It is designated in a circuit by the symbol :
A voltmeter must always be placed in parallel in an electrical circuit because of its high internal resistance.
Realize the electrical circuit of the figure 1, set the direct voltage generator to the value E=6V. Connect the voltmeter to the terminals of a resistance R (positive terminal with the input of R and negative terminal with its output) and measure the value of the voltage across the resistor R using a suitable caliber.
Report the obtained value without forgetting the unit V=………………………….
Remark : The ammeter and the voltmeter are polarized devices, having two positive and negative terminals, their polarities must be respected before connecting them to the circuit. On the other hand, an electrical resistance is not polarized and has an input and an output.
A caliber : Represents the highest value that the device can measure, i.e., the maximum value reached during a measurement.
Use of the multimeter
The multimeter is a device with a digital display which can have several functions depending on the needs of the experimenter: It can be used as an ammeter, voltmeter or ohmmeter (measurement of the value of a resistance). The multimeter contains terminals (see figure 2), terminals D and C are chosen if you want to measure a voltage or resistance, terminals B and C in the case of measuring low currents while A and C for high currents. The COM terminal is equivalent to the negative pole of the multimeter.
Use of the oscilloscope :
An oscilloscope is a device used to analyze with great precision the behavior of a variable and repetitive electrical signal (potential). The oscilloscope screen is nothing more or less than a graph of potential versus time on which we can visualize the behavior of the potential during an entire cycle. The oscilloscope automatically identifies the repeating cycle and displays it motionlessly on the screen (see Oscilloscope Appendix).
- Connect the oscilloscope, the generator and the voltmeter (see first figure of the PW5).
- Complete the table below :
- What is the absolute reading uncertainty committed to the measurement of Vmax ?
- What is the voltage measured by the voltmeter ?
- Calculate:
-- What does VG represent ?
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I - Goal :
· Determination of the value of a resistance by two different methods.
· Verification of the two resistance association laws: Series and parallel associations.
II - Theoretical reminders :
II-1- Ohm's law :
Let U be the voltage drop across a resistance R, it is proportional to the intensity of the current passing through it: U = R.I
II-2- « Color coding » method :
We can see colored rings on a resistance. Each color corresponds to a number (fig.1). We place the resistance so as to have the widest ring (generally gold or silver) to our right.
If, for example, we have 5 rings on a resistance, from left to right: black-red-green-red-green, the corresponding values will then be :
Black = 0, red = 2, green = 5 (significant numbers)
Red = 102 (multiplier)
Green = 0.5 % (tolerance)
The value of the resistance will then be equal to R = 25.102 Ω, with relative uncertainty
ΔR/R = 0.005 (0.5%).
So the resistance value will be displayed in the form : R=(2500.0 ± 12.5) Ω
Remark : If we have a resistance that contains 4 rings, then we will only have 2 significant numbers.
II-3- Kirchhoff's laws :
In an electrical circuit, it is possible to calculate the potential differences across each resistor and the intensity of the direct current in each branch of the circuit by applying Kirchhoff's two laws: the law of nodes and the law of meshes.
II-3-1- Law of nodes :The sum of the intensities of the currents entering through a node is equal to the sum of
the intensities exiting the same node.
In the diagram, for example, we have : i1 + i2 +i3 = i4 + i5
II-3-2- Law of Meshes :
In any mesh, the algebraic sum of the potential differences along the mesh is constantly zero.
In the diagram, we have : V1 + V2 + V3 +V4 = 0
II-4- The different electrical arrangements used :
II-4-1- Electric circuit with a single resistance :
The circuit consists of a resistance of value Rx in series with a generator E. The intensity of the current is measured by an ammeter A which is connected in series. The potential difference between the terminals of the resistance is measured by a voltmeter V which is always connected in parallel.
II-4-2- Electrical circuit with three mounted resistances in series
If the same electric current passes through all three resistances, we say that these latters are in series. In practice, the output of the first resistance must be connected to the input of the second resistance and so on.
II-4-3- Electrical circuit with three mounted resistances in parallel :
If the electric current divides in a node then the resistance are said to be connected in parallel. In practice, the three resistances must have the same input and the same output.
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WHEATSTONE BRIDGE
I - Goal :
The goal of this manipulation is to determine the value of an unknown resistance using the Wheatstone bridge and the wire bridge.
II - Theoretical reminders :
II-1- Wheatstone Bridge :
The Wheatstone bridge consists of an electrical circuit comprising three known resistances and a fourth to be determined, powered by a direct current generator E.
Consider then the circuit below, where R1 and R2 are resistors of known ratio, RV is a known adjustable resistance (rheostat) and RX is the unknown resistance. All of these resistances thus form the so-called Wheatstone bridge. The two points C and D are connected to a galvanometer G.
To determine the value of the unknown resistance RX, it is necessary to adjust the variable resistance RV in the bridge until we manage to cancel the intensity of the current in the branch CD of the bridge.
Therefore, by acting on the resistors R1, R2 and RV it is possible to cancel the current in the galvanometer.
In this case, we can write :
This makes it possible to apply Ohm's law to the terminals of R1 and R2 :
from where :
On the other hand :
Thus :
At the Equilibrium of the bridge, we obtain the relation :
Note that it is useless to know the resistances R1 et R2 ; only their report intervenes
This report is called beachhead report.
II-2- Wire bridge :
The wire bridge is another variant of the Wheatstone bridge. We know that for a homogeneous conducting wire, the resistance is proportional to the length. We can replace R2 and RV by a wire AB (of length L, section S and resistivity ρ) along which a cursor D moves.
In equilibrium, we can write, taking into account the relationship (1)
Where:
RAD is the resistance of the wire of length L1=AD :
RDB is the resistance of the wire of length L2=DB :
By replacing these two values in equation (2), we obtain :
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CHARGING AND DISCHARGING A CAPACITOR
I - Goal :
· Study of the charge and discharge voltages of a polarized capacitor through a resistor and their variations as a function of time.
· Verification of the association laws of polarized capacitors.
II - Theoretical reminders :
II-1- Definition of a capacitor :
A capacitor is made up of two conductive plates carrying opposite electrical charges +q and –q, separated by an insulator. The relationships between the quantities u(t), i(t) and q(t) are algebraic: they depend on the chosen orientation conventions.
II-2- Principle :
The capacitor of capacity C is charged by a direct voltage generator E (the switch K is in position A). It is discharged through resistor R (switch K is in position B) (see Figure 1).
II-3- Case of charging a capacitor :
The capacitor being initially discharged, at time t = 0 we flip the switch K to position A and the capacitor charges via a resistor R. By application of the law of meshes and taking into account the sign conventions at the terminals of the different elements present in the circuit, it is easy to obtain the following relationships :
By deriving this last equation with respect to time we obtain :
Hence the differential equation governing the evolution of the charging voltage as a function of time is:
The solution of this first order differential equation with constant coefficients and constant second member is as follows:
The quantity τ corresponds to the time constant which characterizes the evolution of the state of charge of the capacitor in this circuit. Let E be the voltage applied across the circuit. Flipping the switch K to position A causes the voltage UC to increase and the intensity i to decrease exponentially, as the Capacitor charges (see Figure 2).
II-4- Case of discharge of a capacitor :
The capacitor being initially charged under the potential difference E, we switch K to position B at time t = 0, the capacitor discharges through the resistance R. By proceeding in the same way as that presented in the previous part, the voltage and current intensity in the circuit now follow the laws:
In the RC portion of the circuit the discharge current flows in the opposite direction to the charge current, its absolute value is maximum at t = 0 and decreases exponentially as the capacitor discharges (see figure 3).
III - Case of charging two capacitors :
We want to study the behavior of the charge of two capacitors placed on the one hand in series (see figure 4) and on the other hand in parallel (see figure 5). The experiment in this part consists of measuring the voltage difference across the equivalent capacitor and from the charge curve we deduce the value of the equivalent capacity Ceq in the two types of association.
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USE OF THE OSCILLOSCOPE AND PHASE SHIFT MEASUREMENT
I. GOALS :
- Learn to use the oscilloscope as a means of measurement in the alternating regime.
- Analyze the behavior of a variable and repetitive electrical signal (potential) in the alternating regime.
- Study the behavior of the phase shift in the different associations: resistance-resistance (R-R), resistance-coil (R-L) and resistance-coil-capacitor (R-L-C).
II. EQUIPMENT USED :
- Low frequency generator (GBF).
- Voltmeter or multimeter.
- Two resistances of 1kW et 100W, a capacitor C=1µF and an induction coil L=9mH.
- An oscilloscope.
III. USE OF THE OSCILLOSCOPE :
An oscilloscope is a device used to analyze with great precision the behavior of a variable and repetitive electrical signal (potential). The oscilloscope screen is nothing more or less than a graph of potential versus time on which we can visualize the behavior of the potential during an entire cycle. The oscilloscope automatically identifies the repeating cycle and displays it on the screen.
III-1. Potential measurement
The oscilloscope screen is made up of two perpendicular axes crossing in the middle and divided into small squares (parallel to the axes) of length 1cm. These squares are divided in turn into 5 small divisions. By connecting a signal to the channel input, a curve V(t) appears on the screen where the horizontal axis represents time and the vertical axis represents potential. The measurement of time or potential, corresponding to a point on the plot, has a value equal to the product of the value of the scale with that of the number of divisions. In practice, we measure the peak-to-peak voltage (Vcc) which represents twice the maximum value of the voltage (Vmax).
Questions :
1. .What do the voltage Veff measured by the voltmeter and the maximum voltage Vmax measured by the oscilloscope represent ?
In practice, to measure a voltage with the oscilloscope, you must follow the following steps:
1. Assemble the figure below.
2. Turn on the generator (GBF).
3. Change the frequency by turning the button frequency of the generator.
4. Change the voltage value with the button amplitude of the generator.
5. Turn on the oscilloscope and choose the mode CH1 (chanal1).
6. Check that the CH1 channel switch is in AC (alternatif current).
7. Adjust the 0V level by pressing the button GBD of chanal CH1.
8. Adjust the curve using the vertical and horizontal position buttons.
9. Adjust the voltage gauge to allow a good voltage reading.
III-2. Phase shift measurement
a-Temporal difference method
Here we only define the phase shift of two signals which have the same period. . Let two signals of type :
Where A1 and A2 et are the amplitudes also called peaks.
The frequency is linked to the period by the relation:
The phase shift between two signals is defined by :
Where Δt represents the time difference between the two signals.
Remark : If we define signal 1 as that which passes through the origin O, we can say that :
If OM > 0 : Signal 2 is phase delayed compared to signal 1.
If OM < 0 : Signal 2 is in phase advance compared to signal 1.
b-Lissajous method
In the oscilloscope, we can eliminate the time component of the signals et by pressing the button XY. We obtain an ellipse from which the phase shift between the two signals will be calculated by the formula :
There are special cases for Lissajous curves :
If Δφ = 0 or π : The ellipse is reduced to a line, one of the diagonals of the rectangle.
If Δφ = π/2 or 3π/2 : The axes of the ellipse merge with those of the rectangle.
IV. Manipulation :
Study the phase shifts of the R-R, R-C, R-L and RLC circuits using the two phase shift measurement methods mentioned above.
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ANNEX : OSCILLOSCOPE FRONT PANEL
List of some oscilloscope switches :
(A) The screen : It is made up of tiles measuring 1 cm on each side.
(B) The main axes.
(1) On/Off : Oscilloscope on and off button.
(2) Controls the vertical position of the signal.
(3) Voltage gauge : this switch is used to change the vertical scale. The unit is V/cm, mV/cm, µV/cm.
(4) AC/DC : This switch allows you to adjust the direct current signal (DC, Direct Current) and the alternating current signal (AC, Alternating Current).
(5) GND : It allows the plates to be connected to ground. It also allows you to adjust the level 0V.
(6) Entry port for channel 1.
(7) Entry port for channel 2.
(8) The mode : The majority of oscilloscopes have a dual input, which means that two signals can be viewed at the same time.
(9) Activate the Lissajous curve by pressing the button and choosing the mode CH2 (switch 8).
(10) Time caliber : This switch is used to change the horizontal scale. The unit is s/cm, ms/cm, µs/cm.
(11) Trigger level : For the device to be able to display a signal, it must define an input voltage level from which it will start displaying.
(12) Trigger source : The device must observe signals that repeat periodically. The oscilloscope must start at the same point on the wave function to have a stable image. There are two modes : norm et auto (you have to leave it on auto).
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