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May 24 2019

How to Measure Resistance and How to Detect Resistance?

I Introduction

There are many ways to measure resistance: ohmmeter, volt-ampere, volt-volt, ampere-ampere, bridge, substitution, comparison, half-deviation and so on. No matter what the method is, the experimental principle is no more than partial circuit Ohm's law and closed circuit Ohm's law as well as the basic law of series and parallel circuits. The measurement of each physical quantity should be flexible in application.

Measuring Resistance with a Digital Multimeter


Catalog

I Introduction

II Measuring Resistance with an Ohmmeter

2.1 Structure and Principle of Ohmmeter

2.2 Measurement Method and Steps

2.3 Notes

III Volt Ampere Method

3.1 Definition and Principle

3.2 Operating Steps for Measuring Resistance by Volt-ampere Method

3.3 Selection of Electricity Meter and Sliding Rheostat

3.4 Selection of Voltage Divider and Current Limiting Circuit

3.5 Choice of Internal Connection Method and External Connection Method

IV Electric Meter Half-bias Method for Measuring Resistance

4.1 Ammeter Half-bias Method

4.2 Voltmeter Half-bias Method

V Several Special Methods for Measuring Resistance

5.1 A-A Method and V-V Method

5.2 Formula Calculating Method

5.3 Resistance Measurement by Equivalent Replacement Method                         

5.4 Measuring Resistance with Bridge Circuit

VI Detection Methods of Different Resistors

VII One Question Related to Resistance Measurement


II Measuring Resistance with an Ohmmeter

2.1 Structure and Principle of Ohmmeter

Its circuit is shown in the figure below. It consists of three components: G is an ammeter with internal resistance of Rg and full bias current of Ig. R is a variable resistor, also called a zero-regulated resistor. The battery has an electromotive force of E and an internal resistance of r.

The principle of the ohmmeter is made according to the closed circuit Ohm's law. When the red and black test pens are connected to the resistance Rx to be tested, here can get according to the Ohm's law of the closed circuit:

Formula

R, Rg and r are all fixed-value resistors

There is a one-to-one functional relationship between the current I and the resistance Rx to be measured, so the purpose of measuring the resistance can be achieved by measuring the current. Mark the resistance Rx value corresponding to current I directly on the dial. The resistance value of the measured resistance can be read directly from the dial. Since I and Rx are nonlinear, the scale is not uniform, and since it is a subtractive function, the scale direction is opposite to the current range.

Circuit of Ohmeter

Figure1. Circuit of Ohmeter

2.2 Measurement Method and Steps

1) Mechanical zero adjustment: Check whether the pointer of the multi-purpose electricity meter stops at the zero scale of the dial. If it does not point to zero, a small screwdriver can be used to rotate the positioning screw to make the pointer point to the zero scale of the left current.

2) Choose the right gear: Because the median resistance of the ohmmeter is tens of ohms, and the ohmmeter gauge is used to measure the resistance when the pointer points to the central reading is more accurate, so the selected ratio is one order of magnitude smaller than the estimated value of the resistance to be measured.

3) Ohmmeter zero: short connect the red and black meter pen. Adjust the zero resistance knob to make the pointer point to the zero scale of the ohmmeter. If the "Ohmzero" button can't be turned right after all, the battery in the meter should be replaced.

4) Measurement reading: lap the meter pen at both ends of the resistance to be measured. If the pointer is near the center, the number of the meter needle is multiplied by the ratio, which is the resistance value of the resistance to be measured. If the pointer is close to the left and right ends, the appropriate multiplier can be selected and reset to zero according to the rule of "large range and large Angle deviation, small range and small Angle deviation". Follow steps 3 and 4.

5) After the multi-purpose meter is used up, put the selection switch in the "OFF" or the highest voltage of the alternating voltage, and pull out the meter and pen.

2.3 Notes

① When measuring resistance, put the selector switch in ohm range.

② Select the appropriate magnification gear so that the pointer is near the middle of the dial.

③ Ohme zero must be reset after every gear change.

④ Before measuring the resistance, the resistance to be measured must be disconnected from other circuits.

⑤ Do not hold the metal parts of the two test leads with both hands to measure resistance at the same time.

⑥ When measuring resistance, if the pointer is over the right, the measurement should be changed to a higher gear; if the pointer is over the left, the measurement should be changed to a lower gear.

⑦ After measuring the resistance, pull out the test leads and set the selector switch to OFF or the highest AC voltage.

III Volt Ampere Method

3.1 Definition and Principle

Volt-ampere method (also known as volt-measurement method, ampere-measurement method) is a common method of measuring resistance, by using partial circuit Ohm's law: R=U/I to measure the resistance value. Use the ammeter to measure the current through the unknown resistor at this voltage, and then calculate the resistance of the unknown resistor. Volt-ampere resistance measurement is a common method for directly measuring the resistance of a conductor using an ammeter and a voltmeter. It is roughly divided into two types: inter-connected and exter-connected.

3.2 Operating Steps for Measuring Resistance by Volt-ampere Method

(1) Connect the circuit

a. Select an electricity meter of appropriate range, i.e. a sliding rheostat;

b. Select partial voltage or current limiting circuit;

c. Determine whether to connect internally or externally;

d. Connect the circuit;

(2) Operation

Adjust the sliding rheostat, read the ammeter and voltmeter in turn, and record the table.

(3) Data processing

Method A. Calculate each resistance by mathematical calculation and then calculate the average value to get the resistance value.

Method B. By recording the I and U read respectively on the coordinate paper and establishing the u-I coordinate axis, the value of resistance R was solved by calculating the slope.

3.3 Selection of Electricity Meter and Sliding Rheostat

  • There is a basis for selecting the sliding rheostat in the voltage divider circuit, that is, try to use the sliding rheostat with a smaller total resistance.
  • When the maximum resistance of the sliding rheostat is approximately equal to the resistance of the resistor to be measured, a voltage divider circuit must be selected.
  • When measuring with a voltmeter (ammeter), one must ensure that the measured data cannot exceed the maximum measurement value of the voltmeter (ammeter), and the second is to maximize the accuracy of the measurement on the premise of ensuring the safety of the voltmeter (ammeter), so according to The size of the measured voltage (current) selects the range of the voltmeter (ammeter).
  • When measuring, the maximum measured value of the ammeter or voltmeter should be higher than the actual value of the circuit under test, otherwise it will easily damage the ammeter or voltmeter; but if it is much higher than the actual value of the circuit under test, the reading error will be very large. Taking the pointer meter as an example, the swing angle is limited. When measuring the same circuit, the more the actual maximum measurement value of the ammeter or voltmeter is higher than the actual value of the circuit, the smaller the amplitude of the pointer swing, so the reading error will be The bigger.

3.4 Selection of Voltage Divider and Current Limiting Circuit

(1) Circuit characteristics of current limiting and voltage division

Circuit diagram:

current limiting and voltage division

Figure2. Current Limiting and Voltage Division

The sliding head slides from a to b The voltage variation range on R0 (set r = 0)

Voltage Variation Range

Figure3. Voltage Variation Range

When the electric key is turned on, the initial position of the sliding head in both circuits should be at the a end.

(2) Selection method

① Current limiting connection method (usually)

  • Current and voltage can reach the required adjustment range
  • Do not exceed the range of the measuring instrument
  • Do not exceed the maximum current allowed by each component

②Divided pressure connection method (three special conditions)

a.The voltage or current of a part of the circuit is required to be continuously adjustable from zero.

b.Regardless of how to adjust the sliding rheostat when using the current limiting connection method, the current (voltage) in the circuit will exceed the meter's range or the maximum current allowed by the component.

c.The resistance of the electrical appliance is much greater than the resistance of the sliding rheostat, which is not conducive to measuring and obtaining multiple sets of data.

3.5 Choice of Internal Connection Method and External Connection Method

(1) Selection method

  • When the external method is selected, the voltmeter and the resistance are connected in parallel. The reading of the voltmeter is the voltage across the resistance, but the ammeter measures the total current through the resistance and the voltmeter, so the measured value is less than the true value, the actual measured resistance The value is the resistance of the resistance and resistance in parallel in the voltmeter. If the value of the resistance is much smaller than the internal resistance of the voltmeter, the current divided by the voltmeter is very small, then the current measured by the ammeter is close to the current through the resistor, so the external method is suitable for measuring small resistance.
  • When the internal connection method is selected, the ammeter is connected in series with the resistance. The reading of the ammeter is the current value of the resistance, but the voltmeter measures the total voltage of the resistance and the ammeter, so the measured value is greater than the true value. The total resistance value in series with the resistance in the ammeter. If the value of the resistance is much greater than the internal resistance of the ammeter, the voltage divided by the ammeter is very small, then the voltage measured by the voltmeter is close to the voltage across the resistor, so the internal connection method is suitable for measuring large resistance.
  • Circuit diagrams of current limiting and voltage division, internal connection and external connection

Inter-connected and Exter-connected Circuit

Figure4. Inter-connected and Exter-connected Circuit

IV Electric Meter Half-bias Method for Measuring Resistance

The meter has its own magical aspect-when it is connected to the circuit, it can display its own reading, so we can use its own reading changes (such as semi-bias) to skillfully measure its internal resistance. The half-bias method is often used to measure the internal resistance of the electric meter. For the half-bias method to measure the internal resistance of the meter, there are the following two setting methods:

4.1 Ammeter Half-bias Method

(1) Experimental steps

① Connect the experimental circuit as shown in the figure;

② Open S2, close S1, adjust R1, make the ammeter reading equal to its range Im ;

③ Keep R1 unchanged, close S2, adjust R2 so that the ammeter reading is equal to Im, and then read the value of R2. If R1RA is satisfied, then RA=R2.

(2) Experimental conditions: R1RA

(3) Measurement result: RA measured = R2<RA

(4) Error analysis

When S2 is closed, the total resistance decreases and the total current increases, which is greater than the full bias current of the original ammeter. At this time, the ammeter is semi-biased, so the current flowing through R2 is greater than the current in the branch where the ammeter is located. The resistance of R2 is greater than the ammeter. The resistance of is small, and we regard the reading of R2 as the internal resistance of the ammeter, so the measured internal resistance of the ammeter is too small.

4.2 Voltmeter Half-bias Method

(1) Experimental steps

Voltmeter Half-bias Method

Figure5. Voltmeter Half-bias Method

① Connect the experimental circuit as shown in the figure;

② Adjust the value of R2 to zero, close S, adjust the sliding contact of R1, so that the voltmeter reading is equal to its range Um;

③ Keep the sliding contact of R1 still, adjust R2 to make the voltmeter reading equal to 2(1)Um, and then read the value of R2. If R1RV, RVR2 can be considered.

(2) Experimental conditions: R1RV

(3) Measurement result: RV measuredR2>RV

(4) Error analysis

When the value of R2 gradually increases from zero, the voltage across R2 and the voltmeter will also gradually increase, so when the voltmeter reading is equal to Um, the voltage across R2 will be greater than Um, making R2>RV, resulting in the measurement of RV The value is too large. Obviously, the half-bias voltage method is suitable for measuring the resistance of a voltmeter with a large internal resistance.

V Several Special Methods for Measuring Resistance

5.1 A-A Method and V-V Method

Experimental principle

1. A-A Method(Ammeter difference method)

(1)As shown in Figure a, two ammeters are connected in parallel, and the internal resistance r1(or r2) of the ammeterA1 (or A2) is obtained from I1r1I2r2

(2)As shown in Figure b, the ammeter A1 is connected in parallel with the fixed value resistor R0 and then in series with the ammeterA2. According toI1r1=(I2I1)R0, the internal resistance r1 of A1 is obtained (this method is also called the ammeter difference method to measure the ammeter Internal resistance).

2. V-V Method(Voltmeter difference method)

(1)As shown in Figure C, two voltmeters are connected in series, and according to r1(U1)=r2(U2), the internal resistance of the voltmeter V1 (or V2)is obtained.

(2)As shown in Figure D, the voltmeter V1 is connected in series with the fixed value resistor R0and then connected in parallel with the voltmeter  V2. According to U2U1+r1(U1)R0, the internal resistance of the voltmeter V1 is obtained (this method is also called the voltmeter difference method to measure the voltmeter The internal resistance).

Experiment Principle for Ammeter Difference Method

Experiment Principle for Voltmeter Difference Method

 

Method analysis

Method

Circuit

Experimental condition

Experimental result

A-A Method

Figure a

①The full bias voltages of A1 and A2 are equal or almost the same

r1 or r2 is known

r1=I1(I2)r2 or r2=I2(I1)r1

Figure  b

①The range of A1 is greater than the range of A1

R0 is known

r1=I1((I2-I1)R0)

V-V Method

Figure  c

①The full bias currents of V1 and V2 are equal or almost the same

r1 or r2 is known

 

r1=U2(U1)r2r2=U1(U2)r1

Figure  d

①The range of V2 is greater than the range of V1

R0 is known

r1=U2-U1(U1)R0

 

5.2 Formula Calculating Method

It mainly applies the characteristics of series-parallel circuit and the knowledge of the whole circuit to analyze and calculate the value of the resistance to be measured. Figure 18 is a circuit for measuring resistance Rx. Rx is the resistance to be measured, R is the protective resistance, and its resistance value is unknown. R1 is the fixed resistance known. The power supply electromotive force is unknown. S1 and S2 are single-pole double-throw switches. A is a current meter with no internal resistance.

Formula Calculating Method

Figure6. Formula Calculating Method

(1)Measuring Rx: S2 closes to d, S1 closes to a, and record the ammeter reading I1; then S2 closes to c, S1 closes to b, and record the ammeter reading I2.

(2)The formula for calculating Rx is:

Formula

When S2 is connected to d and S1 is connected to a, the voltage of Rx is: Ux=I1Rx.

When S2 is connected to c and S1 is connected to b, the voltage U1=I2R2 on R1 does not change the resistance R, Ux=U1

So I1Rx=I2R1

SoFormula

5.3 Resistance Measurement by Equivalent Replacement Method

[Method Interpretation] Equivalent substitution method for measuring resistance: When measuring a resistance (or the internal resistance of an ammeter or voltmeter), replace the resistance to be measured with a resistance box, if the two have the same effect on the circuit (such as equal current or voltage) ), the resistance to be tested is equivalent to the resistance box.

(1) Current equivalent replacement

The experimental steps of this method are as follows:

① Connect the circuit as shown in the circuit diagram, and adjust the resistance of the resistance box R0 to the maximum, and the slider P of the sliding varistor is placed at the a end.

Current Equivalent Replacement Method

Figure7. Current Equivalent Replacement Method

② Close the switches S1 and S2, adjust the slide P so that the pointer of the ammeter is in the proper position, and note that the indication of the ammeter at this time is I.

③ Open the switch S2, and then close the switch S3, keeping the position of the sliding rheostat slider P unchanged, adjust the resistance box, so that the indication of the ammeter is still I.

④ At this time, the resistance value R0 of the resistance box connected to the circuit is equivalent to the resistance value of the unknown resistor Rx, that is, RxR0.

(2) Equivalent replacement of voltage

The experimental steps of this method are as follows:

Equivalent Replacement of Voltage

Figure8. Equivalent Replacement of Voltage

① Connect the circuit as shown in the circuit diagram, and adjust the resistance value of the resistance box R0 to the maximum, and the slider P of the sliding rheostat is placed at the a end.

② Close the switches S1 and S2, adjust the slide P so that the pointer of the voltmeter is in the proper position, and record the indication of the voltmeter as U at this time.

③ Open S2, and then close S3, keeping the position of sliding rheostat slider P unchanged, adjusting the resistance box so that the indication of the voltmeter is still U.

④ At this time, the resistance value R0 of the resistance box connected to the circuit is equivalent to the resistance value of the unknown resistor Rx, that is, RxR0.

5.4 Measuring Resistance with Bridge Circuit

(1)Principle:

The circuit shown in the figure below is called a bridge circuit. Generally, a current flows through the galvanometer, but when a certain condition is met, no current flows through the galvanometer. In this case, it is called bridge balance. When the bridge is balanced, the two potentials of A and B are equal, so the circuit structure can be regarded as: R1R2 and R3R4 are connected in series and then connected in parallel; or R1R3 and R2R4 are connected in parallel, and then connected in series.

Bridge Circuit

Figure9. Bridge Circuit

the condition of the bridge balance: R1×R4=R2×R3

(2)The measuring method:

As shown in Figure 20, connect the circuits, take R1, R2 as a fixed value resistor, R3 is a variable resistance box (can directly read the value), and Rx is the resistance to be tested. Adjust R3 so that the reading in the ammeter is zero, and apply the equilibrium condition to get the value of Rx.

Note: Two points should be paid attention to when measuring the resistance by the bridge method. One is to clarify the structure of the circuit. In the circuit, four resistors are connected in series two by two, and then the ammeter is connected in the middle string, then the part of the series ammeter is "Bridge", the second is to clarify the conditions of electric bridge balance.

VI Detection Methods of Different Resistors

(1)Detection of the Fixed Resistor

①The actual resistance value can be detected by connecting the two test pens (not positive or negative) to the two ends of the resistor. In order to improve the measurement accuracy, the range should be selected according to the nominal value of the measured resistance. Due to the nonlinear relationship of the ohmic scale, its middle section is finer. Therefore, the pointer indication value should be lowered to the middle part of the scale as far as possible, in the range of 20%-80% radian at the beginning of the full scale, so as to make the measurement more accurate. It varies according to the error level of resistance. The errors between the reading and the nominal resistance are allowed to be (+5%), (+10%) or (+20%) respectively. If not, beyond the error range, it means that the resistance value has changed.

②Note: during testing, especially when measuring resistances with resistance values above tens of kΩ, do not touch the conductive parts of the pen and resistors; the detected resistance is soldered from the circuit, at least one head must be soldered to avoid other components in the circuit. It affects the test and causes measurement error. Although the resistance of the color ring resistor can be determined by the color circle mark, it is better to test the actual resistance value with a multimeter when using it.

Related Post: Chip Fixed Resistors

(2) Detection of the Cement Resistor

The method and precautions for testing cement resistance are exactly the same as those for testing ordinary fixed resistors.

Related Post: You can see more about cement resistors in another article about resistor types.

(3)Detection of the Fuse Resistor

In the circuit, when the fuse resistor is melted and disconnected, it can be judged according to experience: if the surface of the fuse resistor is found to be black or burnt, it can be concluded that its load is too heavy, and the current passing through it exceeds the rated value many times; if the surface is open without any trace, it means that the current flowing is just equal to or slightly larger than its rated blown value. The judgment of the fuse resistor with no trace on the surface can be measured by the Rx1 gear of the multimeter. To ensure accurate measurement, one end of the fuse resistor should be soldered from the circuit. If the measured resistance is infinite, it means that the fuse resistor has failed open circuit. If the measured resistance value is far from the nominal value, it indicates that the resistance value is not suitable for reuse. In the maintenance practice, it is found that there are also a few blown resistors that are short-circuited in the circuit, so attention should be paid to the detection.

Ohmmeter

Figure10. Ohmmeter

(4) Detection of the Potentiometer

When checking the potentiometer, first turn the handle to see if the rotation of the handle is smooth, whether the switch is flexible, whether the “click” sound is clear when the switch is turned on or off, and listen to the internal contact point of the potentiometer and the friction of the resistor body. If there is a "rustling" sound, it means that the quality is not good. When testing with a multimeter, first select the appropriate electrical blocking position of the multimeter according to the resistance of the potentiometer to be tested, and then perform the detection as follows.

①Use the ohmic gear of the multimeter to detect the "1" and "2" ends. The reading should be the nominal resistance of the potentiometer. If the pointer of the multimeter does not move or the resistance value is different, it indicates that the potentiometer is damaged.

②Check if the movable arm of the potentiometer is in good contact with the resistor. Detecting the ends of "1", "2" (or "2", "3") with the ohmic gear of the multimeter, and turning the axis of the potentiometer counterclockwise to the position close to the button “off”, the smaller the resistance value, the better.

(5)Detection of the Positive Temperature Coefficient Thermistor

①Room temperature detection (indoor temperature is close to 25 ℃): the actual resistance value of the two pins in contact with PTC thermistor is measured, and compared with the nominal resistance value, the difference between the two is normal within ±2 Ω. If the actual resistance value is too different from the nominal resistance value, the performance of the actual resistance value is poor or damaged.

②Heating detection: on the basis of normal temperature test, the second step of test-heating detection can be carried out, and a heat source (such as electric soldering iron) can be heated near PTC thermistor. At the same time, the multimeter is used to monitor whether the resistance value increases with the increase of temperature. If the thermistor is normal and if the resistance value does not change, it means that its performance becomes worse and can not be used further. Be careful not to keep the heat source too close to or directly in contact with the PTC thermistor to prevent it from being burned.

(6)Detection of the Negative Temperature Coefficient Thermistor

①The method of measuring the NTC thermistor with a multimeter is the same as the method of measuring the ordinary fixed resistor, that is, the actual value of Rt can be measured directly by selecting the appropriate electrical barrier according to the nominal resistance value of NTC thermistor. However, since the NTC thermistor is very sensitive to temperature, the following points should be paid attention to when testing:

  • Rt is measured by the manufacturer at an ambient temperature of 25 ° C. Therefore, when measuring Rt with a multimeter, it should also be carried out when the ambient temperature is close to 25 ° C to ensure the reliability of the test.
  • The measured power shall not exceed the specified value to avoid measurement errors caused by current thermal effects.
  • Pay attention to the correct operation: when testing, do not hold the thermistor body with your hands to prevent the body temperature from affecting the test.

②First, the resistance value Rt1 is measured at room temperature t1, and then the electric iron is used as a heat source, and the resistance value RT2 is measured near the thermistor Rt. At the same time, the average temperature t2 of the surface of the thermistor RT is measured by a thermometer.

(7)Detection of the Varistor

Set the multimeter in 10K gear and connect the pen to both ends of the resistor. The multimeter should show the resistance value indicated on the varistor. If the value exceeds this value, it indicates that the varistor has been damaged.

The varistor can be changed from MΩ (megaohms) to mΩ (milliohms) as the voltage applied to it increases. When the voltage is low, the varistor works in the leakage current region, exhibits a large resistance, and the leakage current is small. When the voltage rises into the nonlinear region, the current changes within a relatively large range, and the voltage does not change much. It exhibits better voltage limiting characteristics; the voltage rises again, and the varistor enters the saturation region, exhibiting a small linear resistance. Due to the large current and the long time, the varistor will overheat and burn or even burst.

(8)Detection of the Photoresistor

①The black light film is used to cover the light-transmitting window of the photoresistor. At this time, the pointer of the multimeter is basically kept, and the resistance is close to infinity. The larger the value, the better the photoresistor performance. If this value is small or close to zero, the photoresistor has been burned through and can no longer be used.

②A light source is aligned with the light-transmitting window of the photoresistor, and the pointer of the multimeter should have a large amplitude swing, and the resistance value is significantly reduced. The smaller the value, the better the photoresistor performance. If the value is large or infinite, it indicates that the open circuit of the photoresistor is damaged and cannot be used any more.

③The light-receiving window of the photoresistor is aligned with the incident light, and the small black paper is shaken on the upper part of the light-shielding window of the photoresistor to be intermittently received by the light. At this time, the pointer of the multimeter should swing left and right with the shaking of the black paper. If the multimeter pointer is always stopped at a certain position and does not oscillate with the paper shake, it indicates that the photosensitive material of the photoresistor has been damaged.

Question: 

Given a Wheatstone-bridge with external voltage V, Resistance Bridge with resistances P, Q, R, S, and galvanometer G. What is the balancing condition of bridge?
Circuit
a) P⁄Q=S⁄R
b) P⁄S=R⁄Q
c) P = R⁄Q
d) S = R⁄Q

Answer: a

Explanation: A Wheatstone bridge is said to be balanced when galvanometer shows null deflection that is zero current flow through that path.

 

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