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Electricity

# ELECTRICAL VOLTAGE #### 1.1 Concept of electrical voltage

Each point of an electric circuit is associated with a value called electric potential (the unit of which is the volt V).

This value depends on an arbitrary constant, to eliminate the latter we always use in practice the voltage which is the potential difference between two points.

Voltage = Difference in potential between two points.

The voltage between the points A and B of the circuit is noted UAB and is equal to: UAB = potential in A – potential in B

#### 1.2 Maintenance of oscillations of an RLC circuit

To measure the voltage between points A and B of a circuit, we mount a voltmeter in shunt between these two points.

The tension is an algebraic quantity, it means that it can be either positive or negative.

Moreover, whatever the points A and B of a circuit, we have the relation: UAB = – UBA

We have seen that for all points A and B of a circuit, the voltage UAB was in fact equal to the potential difference between A and B.

By convention, the potential at a point P is denoted VP (and is expressed in volts).

We therefore have UAB = VA-VB = – (VB-VA) = – UBA

The voltage is represented by an arrow segment and the tip of the arrow goes to the first mentioned terminal.

Example:
The voltage across a connecting wire is zero.
At the terminals of a closed switch the voltage is always zero, but at the terminals of an open switch it is generally not zero.

#### 1.3 The properties of tension

##### Case of dipoles mounted in series:

If the two dipoles (A, B) and (C, D) are associated in series, then according to the law of additivity of voltages for dipoles connected in series we have: UAC = UAB + UBC.

##### Case of dipoles mounted in shunt:

If dipoles (A, B), (C, D) are connected in shunt then the voltage measured at their terminals is the same: UAB = UCD = UEF.

##### What is a node?

A node is a point of the circuit which is connected to at least 3 conductors, it is a kind of crossroads of the electrical circuit.

##### In shunt or in series?

Dipoles are mounted in series if no node separates them, so they are most often on the same line.

Dipoles are branched out if they are connected between the same two nodes. To go from one to the other we have to go through a knot.

##### How to start an exercise including the diagram of a montage?
• Always represent on the diagram the arrows of the known voltages
• Name all the points of the circuit
Look for knots
• Distinguish between series connections and branch connections
• Do not forget to state each time you apply it the law of tensions to be applied and the literal expression in the case studied
• Connections of a voltmeter: The connections must be made in the V and COM “holes”
• To measure the voltage UAB at the terminals of a dipole (A, B), we must connect V> A and COM> B
• If the circuit has a mass then all the points connected by a wire to the mass have a zero electric potential.

### 2 VIEW THE ELECTRICAL VOLTAGE USING AN OSCILLOSCOPE

#### 2.1 How to use an oscilloscope?

##### Connections :

One connects a battery (dipole P, N) to the oscilloscope according to the assembly.

Terminal P connected to input E of the oscilloscope, terminal N connected to ground M of the oscilloscope.

##### The oscilloscope operating modes:
• X – Y mode: A spot appears on the screen, it must then be placed in the center of the screen. By varying the batteries, and therefore the voltages, we see that: UEM = k * Y
– Y: the deviation of the spot
– k: the vertical sensitivity of the oscilloscope (expressed in Volt per division, V.Div-1)
• Scanning mode: a horizontal light line is found at the same level as the spot observed in X-Y mode.

#### 2.2 Visualization of a variable voltage

We keep the same assembly and we see with the mode:

• X – Y: the spot moves vertically, if the frequency is increased a vertical segment appears
• Scanning: the trace is not horizontal, the voltage is therefore variable
In Scan mode, an oscilloscope allows you to see the evolution of a voltage over time.

### 2.3 RELATIONSHIPS FOR A VARIABLE TENSION

• UMAX = Extreme value displayed on the ordinate on the oscillogram, vertical sensitivity.
• Ueff (rms voltage) = UMAX / root (2).
• Period T = h * X
h = horizontal sensitivity in seconds per division,
X: number of divisions corresponding to a period.
• Frequency f = number of periods per second.
f = 1 / T, T is expressed in seconds and f in Hertz (Hz).
• Peak-to-peak voltage UCC: difference between the maximum value and the minimum value (in Volts).