ASSOCIATION OF RESISTANCES IN SERIES AND PARALLEL
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.
