Current generator
A current generator imposes an intensity Im through the unknown resistance Rx, we measure the voltage Vm appearing at its boundaries.
Such an assembly does not make it possible to measure with precision resistances whose value exceeds a few kΩ because the current in the voltmeter

Analog voltmeter

They usually consist of a millimeter ammeter in series with high resistance. Analog voltmeters

is then no longer negligible
(the internal resistance of the voltmeter

Analog voltmeter

They usually consist of a millimeter ammeter in series with high resistance. Analog voltmeters

is generally 10 MΩ).
The assembly is therefore completed by an auxiliary current generator controlled to the value of the voltage measured by the voltmeter

Analog voltmeter

They usually consist of a millimeter ammeter in series with high resistance. Analog voltmeters

and responsible for delivering the current in the voltmeter

Analog voltmeter

They usually consist of a millimeter ammeter in series with high resistance. Analog voltmeters

.
When the value of the resistance Rx is less than ten ohms, to avoid taking into account the various connection resistors, it is necessary to implement a special assembly, carried out in the ohmmeters 4 strands.

The ideal voltage generator is a theoretical model.
It is a dipole capable of imposing a constant voltage regardless of the load connected to its terminals.
It is also called a voltage source.
An ammeter is used to measure the current I circulating in a resistor Rx to which a low voltage is applied V Defined.
This method is used in analog ohmmeters equipped with galvanometers with a movable frame.

Here is an example of typical use of a commercial ohmmeter.
Use one of the calibres in the green zone.
We have the choice between
- 2 MΩ
- 200 kΩ
- 20 kΩ
- 2 kΩ
- 200 Ω

Currently, nothing is connected to the two terminals of the ohmmeter, we measure the resistance of the air between these two terminals. This resistance is greater than 2 MΩ.
The ohmmeter cannot give the result of this measurement, it displays 1 on the left of the screen.

If we have no idea of the value of the resistance to be measured, we can keep the caliber 2 MΩ and make a first step.
If we know the order of magnitude of the resistance, we choose the size just above the estimated value.

When the resistor is used in a mount, it must be extracted from it before connecting it to the ohmmeter.
The resistance to be measured is simply connected between the terminal COM and the terminal identified by the letter Ω.
Reading the result
Here, for example, we read :
R = 0,009 MΩ
in other words R = 9 kΩ

Since the value of the resistance is of the order of 9 kΩ, one can adopt the caliber 20 kΩ.
We then read :
R = 9,93 kΩ
The following calibre (2 kΩ) is less than the value of R. So we will not be able to use it.

Consistency of the result of the measurement with the value marked on the body of the resistance
The value of the resistance is indicated by three colored bands.
A fourth strip indicates the accuracy of the marking. Here, this gold color band means that the accuracy is 5%.

Each color corresponds to a number :

Here the marking indicates :
R = 10 × 10³ Ω at 5% near.
either : R = 10 kΩ at 5% near.
5% from 10 kΩ = 0,5 kΩ.

Resistance R is therefore included in the interval :
9,5 kΩ ≤ R ≤ 10,5 kΩ
The result of the measurement R = 9,93 kΩ is well compatible with marking. We can finally write :
R ≈ 9,9 kΩ

An ohmmeter does not allow high-precision measurements. If we want to reduce the uncertainties, there are methods of comparing resistances using bridges.
The most famous is the Wheatstone Bridge.

It is necessary to have a continuous generator, a galvanometer g, calibrated resistors R₁ and R₂ and calibrated adjustable strength R₄.
R₁ and R₂ of the one part and R₃ and R₄ on the other hand constitute dividers of the tension E of supply to the bridge.

Resistance is settled R₄ to obtain a zero deviation in the galvanometer to balance the bridge.

R_1,R_2,R₃ and R₄ are the resistances crossed respectively by the intensities I_1,I_2,I₃ and I_4.

        UCD

Operation

= R x I     What if     I = 0     alors     UCD

Operation

= 0
        UCD

Operation

= U_CA + U_AD
        0 = - R₁ x I₁ + R₃ x I₃
        R₁ x I₁ = R₃ x I₃     equation 1


        UCD

Operation

= U_CB + U_BD
        0 = R₂ x I₂ - R₄ x I₄
        R₂ x I₂ = R₄ x I₄     equation 2

According to the law of knots :

        I₁ + I = I₂ What if I = 0 => I₁ = I₂
        I₃ = I + I₄ et si I = 0 => I₃ = I₄

We will therefore have by making the report of the equations 1 / 2

        ( R₁ x I₁ ) / ( R₂ x I₂ ) = ( R₃ x I₃ ) / ( R₄ x I₄ )
        R₁ / R₂ = R₃ / R₄     you find the product in cross.

If the resistance to be determined Rx is in place of R₃, then :

        R_X = R₃ = ( R₁ / R₂ ) x R₄

So : at the equilibrium of the bridge, the cross products of the resistors are equal

The wire bridge is a variant of the Wheatstone Bridge.
No need for calibrated adjustable resistance. It is sufficient a resistor R of precision preferably having a resistance of the same order of magnitude as that of the unknown resistor and a homogeneous resistant wire and of constant section which one tends between two points A and B.
A contact is moved along this wire until a zero current is obtained in the galvanometer.
The resistance of a wire being proportional to its length, one can easily find the resistance R_x unknown after measuring lengths L_a and L_b.

As wire, constantan or nichrome is used with a section such that the total resistance of the wire is of the order of 30 Ω.
To obtain a more compact device, it is possible to use a multi-turn potentiometer.
It is possible to use a wire bridge to make a Wheatstone bridge.
A zero detector is connected between the bridge slider and the common point of a standard resistor R and unknown resistance R_x.
The contact is moved C along the wire until a zero value is obtained in the detector.
When the bridge is in equilibrium, we have :

        R_a x R_x = R_b x R

The strength of a wire being proportional to its length, the ratio R_b / R_a is equal to the ratio K lengths L_b / L_a.

Finally, we have :

        R_x = R x K

To make this method more concrete, here is a dynamic digital simulator.
Vary the value of R and the report L_b / L_a with the mouse to cancel the tension of the bridge and find the value of R_x.
DIY : Check the theory.