Name the different methods of finding unknown resistance
Answers
Answered by
2
Measuring with a multimeter
The most obvious way to measure the resistance is by using a multimeter set at the resistance range. In most cases this gives a reliable result. Only when measuring low ohmic resistances the fault becomes unacceptable due to the test lead and contact resistance. At high ohmic resistors the leak resistance plays a significant role. This will be discussed in detail in the following chapters.
The resistance measuring principle is clarified by the methods used in multimeters.
Passive multimeters
Fig. 2: Resistance measurement with a passive multimeter.
The most multimeter models provide with a moving coil meter measure the resistance as follows: The unknown resistor Rtest is placed in series with the range resistance Rb and the moving coil meter A and is connected to a voltage source Vs as shown in figure 2.
The current trough the meter is calculated as:
[A]
This shows that the meter indication which is proportional with the current is non-linear. This explains the aberrant resistance scale that comes with these instruments. Rd in the equation is the moving coil meter resistance. The resistance Rm is the replacement resistance for the test leads and contact resistances. Because these resistances don't have a constant value, the uncertainty of low ohmic measurements is relative high.
Active multimeters
Fig. 3: Resistance measurement with an active multimeter.Digital multimeters and active analog types measure the resistance by feeding a known current I through the the resistor under test and measure the voltage across it. The principle of this measurement is shown in figure 3.
The voltage that is measured by the voltmeter V is:
[V]
When the test lead resistance Rm is ignored, the linear correlation between the resistance and measured voltage is clearly visible. The voltmeter must have a very high input resistance. Especially when high ohmic resistors are measured, this input resistance will play a significant role and make the result unreliable. Also here shall the test lead and contact resistance influence the accuracy, especially when measuring low ohmic resistors.
Four terminal sensing
Fig. 4: Resistor measured with a four terminal sensing arrangement.
As mentioned before the test lead and contact resistance may not be neglected when measuring low resistances. A value of 1 Ω for this extra introduced resistance in not uncommon. This can easily be tested by setting the multimeter in the lowest resistance range and holding the two test pins together.
If the resistance must be measured with an uncertainty smaller than 1%, than it's impossible to do this at resistances smaller than 100 Ω with an ordinary multimeter. Because the measure current of a multimeter flows through the test leads and contacts, it will cause extra voltage drops which are included in the measurement. A four terminal measurement eliminates these kind of faults by separating the current injection circuit and the voltage measurement circuit.
Using a current source
Fig. 5: Principal circuit for a low ohmic resistance measured with a four terminal sensing arrangement.
The resistor to be measured Rtest is connected to a current source Ib. By using a current source the test leads and contact resistance Rv don't influence the current through the resistor under test. The voltage across the unknown resistor is measured with a second circuit. Because this voltage is measured with a voltmeter V with a high input impedance, there will flow almost no current in this circuit. Therefore the voltage drop across the test leads and contacts resistances Rm is neglectable.
The unknown resistance can be calculated with ohms law:
[Ω]
To improve the accuracy, the voltage must be measured as close as possible to the test object, and the current must be injected at a point away from the the test object
The most obvious way to measure the resistance is by using a multimeter set at the resistance range. In most cases this gives a reliable result. Only when measuring low ohmic resistances the fault becomes unacceptable due to the test lead and contact resistance. At high ohmic resistors the leak resistance plays a significant role. This will be discussed in detail in the following chapters.
The resistance measuring principle is clarified by the methods used in multimeters.
Passive multimeters
Fig. 2: Resistance measurement with a passive multimeter.
The most multimeter models provide with a moving coil meter measure the resistance as follows: The unknown resistor Rtest is placed in series with the range resistance Rb and the moving coil meter A and is connected to a voltage source Vs as shown in figure 2.
The current trough the meter is calculated as:
[A]
This shows that the meter indication which is proportional with the current is non-linear. This explains the aberrant resistance scale that comes with these instruments. Rd in the equation is the moving coil meter resistance. The resistance Rm is the replacement resistance for the test leads and contact resistances. Because these resistances don't have a constant value, the uncertainty of low ohmic measurements is relative high.
Active multimeters
Fig. 3: Resistance measurement with an active multimeter.Digital multimeters and active analog types measure the resistance by feeding a known current I through the the resistor under test and measure the voltage across it. The principle of this measurement is shown in figure 3.
The voltage that is measured by the voltmeter V is:
[V]
When the test lead resistance Rm is ignored, the linear correlation between the resistance and measured voltage is clearly visible. The voltmeter must have a very high input resistance. Especially when high ohmic resistors are measured, this input resistance will play a significant role and make the result unreliable. Also here shall the test lead and contact resistance influence the accuracy, especially when measuring low ohmic resistors.
Four terminal sensing
Fig. 4: Resistor measured with a four terminal sensing arrangement.
As mentioned before the test lead and contact resistance may not be neglected when measuring low resistances. A value of 1 Ω for this extra introduced resistance in not uncommon. This can easily be tested by setting the multimeter in the lowest resistance range and holding the two test pins together.
If the resistance must be measured with an uncertainty smaller than 1%, than it's impossible to do this at resistances smaller than 100 Ω with an ordinary multimeter. Because the measure current of a multimeter flows through the test leads and contacts, it will cause extra voltage drops which are included in the measurement. A four terminal measurement eliminates these kind of faults by separating the current injection circuit and the voltage measurement circuit.
Using a current source
Fig. 5: Principal circuit for a low ohmic resistance measured with a four terminal sensing arrangement.
The resistor to be measured Rtest is connected to a current source Ib. By using a current source the test leads and contact resistance Rv don't influence the current through the resistor under test. The voltage across the unknown resistor is measured with a second circuit. Because this voltage is measured with a voltmeter V with a high input impedance, there will flow almost no current in this circuit. Therefore the voltage drop across the test leads and contacts resistances Rm is neglectable.
The unknown resistance can be calculated with ohms law:
[Ω]
To improve the accuracy, the voltage must be measured as close as possible to the test object, and the current must be injected at a point away from the the test object
Similar questions