Accurate Wheatstone Bridge Resistance Measurement: Structure, Schematic, & Equation Analysis

Hello,
Could you please check if the answers to the questions are right.

Task 1
What is a Wheatstone Bridge for?
A: The Wheatstone bridge, thanks to its structure, enables resistance measurement with high accuracy (from 1 ? to 10 M? . With the help of the three internal resistances of the bridge (knowing their resistance), we can calculate the resistance of the connected element.

Exercise 2
Draw a schematic diagram of the Wheatstone bridge and derive the equation for measuring the resistance with this bridge.
Re:
U1 = U3, U2 = U4, U1 = R1 * I1, U2 = R2 * I1, U3 = R3 * I2, U4 = R4 * I2 -> R1 * I1 = R3 * I2, R2 * I1 = R4 * I2 - -> R1 = (R2 * R3) / R4

Exercise 3
Why is this equation not completely accurate and why do we accept this state of affairs?
A: This equation is not complete because the formulas do not take into account the voltage drops on the eight sections of the wires connecting the resistances.
We accept this state of affairs because the inaccuracy is not significant as long as the resistances of the bridge resistors are well above the resistance of the connecting wires.

Task 4
What role does the galvanometer play in the bridge?
A: Magnetoelectric galvanometer (zero detector) (pointer instrument) is used to detect the equilibrium state of the bridge. (After setting which it can be removed from the system).

Task 5
What is the equilibrium state of the sternum and how is this state achieved in practice?
A: The equilibrium state of the bridge is a state in which the potential difference between points A and B becomes zero (the Ig current disappears). This state is achieved by adjusting the resistances R2, R3, R4. This adjustment is called balancing the bridge. Uab = 0

Task 6
Derive the formula for the relative limit error of the resistance measurement with the Wheatstone bridge.
Re:


Task 7
Write a definition of the absolute and relative bridge dead-band error.
A: The absolute bridge insensitivity error ?n is the largest increase in the measured resistance ?R1, at which the galvanometer reading is still equal to zero. This is theoretical.
In practice, it is the increase in the measured resistance ?R1, causing the smallest perceptible displacement of the galvanometer pointer ?a. It is assumed that ?a = 0.1 mm. | ?n | = | ?R1 | when ?a = 0.1mm.
The relative insensitivity error of the bridge ?n is the quotient: | ?n | = | ?n / R1 |.

Task 8
Describe the course of the experimental determination of the insensitivity error.
A: Experimental determination of the insensitivity error requires the realization of increases in the measured resistance R1, which is most often an unregulated element. Therefore, in practice, the equivalent insensitivity error is determined by applying the relative and absolute error to the resistance R3, which is a six-decade laboratory resistor, enabling the implementation of
very small increases in resistance (?R = 0.1? .

Task 9
Can I measure a current-dependent (nonlinear) resistance with a Wheatstone bridge?
A: You cannot, because it is used to measure the linear resistance with the knowledge of the parameters of the other linear resistances included in the bridge.

Hello,

michael2303 wrote:

Hello,
Could you please check if the answers to the questions are right.

Task 1
What is a Wheatstone Bridge for?
A: The Wheatstone bridge, thanks to its structure, enables resistance measurement with high accuracy (from 1 ? to 10 M? . With the help of the three internal resistances of the bridge (knowing their resistance), we can calculate the resistance of the connected element.

It is also worth adding that it is used to measure double-terminal resistors in an indirect way, mostly (excluding technical bridges), and to mention - qualitatively - about the measurement method.

michael2303 wrote:

Exercise 2
Draw a schematic diagram of the Wheatstone bridge and derive the equation for measuring the resistance with this bridge.
Re:
U1 = U3, U2 = U4, U1 = R1 * I1, U2 = R2 * I1, U3 = R3 * I2, U4 = R4 * I2 -> R1 * I1 = R3 * I2, R2 * I1 = R4 * I2 [ by dividing the parties - perm. Quarz ] -> R 1 / R 2 = R. 3 / R 4 -> R1 = (R2 * R3) / R4

Correct, although it should be named correctly in the question equilibrium condition of the Wheatstone bridge .

michael2303 wrote:

Exercise 3
Why is this equation not completely accurate, and why do we accept this state of affairs?
A: This equation is not complete because the formulas do not take into account the voltage drops on the eight sections of the wires connecting the resistances.
We accept this state of affairs because the inaccuracy does not make the signifier measurement errors as long as the resistances of the bridge resistors significantly exceed the resistance of the connecting cables.

Correct answer.

michael2303 wrote:

Task 4
What role does the galvanometer play in the bridge?
A: Magnetoelectric galvanometer (zero detector) (pointer instrument) is used to detect the equilibrium state of the bridge. (After setting which it can be removed from the system).

Correct, but why remove the galvanometer when the bridge is in equilibrium?

michael2303 wrote:

Task 5
What is the equilibrium state of the sternum and how is this state achieved in practice?
A: The equilibrium state of the bridge is a state in which the potential difference between points A and B becomes zero (the Ig current disappears). This state is achieved by adjusting the resistances R2, R3, R4. This adjustment is called balancing the bridge. Uab = 0

Correct. As a rule, adjustment is carried out with only one resistor, after preselecting the resistance values of the other two branches.

michael2303 wrote:

Task 6
Derive the formula for the relative limit error of the resistance measurement with the Wheatstone bridge.
Re:

The final formula is correct, but reaching it can be calculated much simpler - without removing the expression in front of the parentheses: R 4 / (R 2 o R 3 ).

michael2303 wrote:

Task 7
Write a definition of the absolute and relative bridge dead-band error.
A: The absolute bridge insensitivity error ?n is the largest increase in the measured resistance ?R1, at which the galvanometer reading is still equal to zero. This is theoretical.
In practice, it is the increase in the measured resistance ?R1, causing the smallest perceptible displacement of the galvanometer pointer ?a. It is assumed that ?a = 0.1 mm. | ?n | = | ?R1 | when ?a = 0.1mm.
The relative insensitivity error of the bridge ?n is the quotient: | ?n | = | ?n / R1 |.

Correct, but it is worth adding information that this applies to a galvanometer with a millimeter scale.
There are galvanometers of a different design, graduated in divisions, etc.

michael2303 wrote:

Task 8
Describe the course of the experimental determination of the insensitivity error.
A: Experimental determination of the insensitivity error requires the realization of increases in the measured resistance R1, which is most often an unregulated element. Therefore, in practice, the equivalent insensitivity error is determined by applying the relative and absolute error to the resistance R3, which is a six-decade laboratory resistor, enabling the implementation of
very small increases in resistance (?R = 0.1? .

Correct, although you can - for this purpose - replace a resistor measured with an accurate decade resistor.
It should also be noted that the above-mentioned insensitivity error also depends on the value of the bridge supply voltage and the sensitivity of the galvanometer used, as well as on the selection of the resistance value of the individual branches of the bridge so that they meet the equilibrium condition for a given value of the measured resistance.

michael2303 wrote:

Task 9
Can I measure a current-dependent (nonlinear) resistance with a Wheatstone bridge?
A: No. , no it is possible, because it is used to measure the linear resistance with the knowledge of the parameters of the remaining linear resistances included in the bridge.

Correct answer.

PS I corrected some editorial shortcomings.

Thank you