- Resistance Definition: Resistance is the opposition to electric current flow, a fundamental concept in electrical engineering.
- Measurement of Low Resistance: Low resistances (<1Ω) are measured using methods like Kelvin’s Double Bridge to minimize error from contact resistance.
- Measurement of Medium Resistance: For medium resistances (1Ω to 100kΩ), the Wheatstone Bridge Method is a standard, balancing the circuit to detect resistance without current flow.
- Measurement of High Resistance: High resistances (>100kΩ) are measured with techniques that control for leakage currents and electrostatic effects, ensuring more accurate results.
- Common Measurement Challenges: Key issues in the measurement of resistance include the impact of contact resistance, electrostatic charges, and leakage currents that can skew results.
Resistance values in electrical and electronics engineering span from the very low (a transformer winding) to the very high (the insulation resistance of those same windings). A multimeter gives only a rough estimate; precise measurement, especially near either extreme, needs a specific method. The sections below group the main measuring methods into three classes.
Measurement of Low Resistance (<1Ω)
A major challenge in measuring low resistance values is the contact or lead resistance of the measuring instruments themselves. Although small, that resistance compares with the value being measured and produces appreciable error.
To eliminate this issue, small-value resistors are built with four terminals: two carry the current and two sense the potential.
The figure below shows this construction.
The current flows through current terminals C1 and C2, while the potential drop is measured across potential terminals V1 and V2. The unknown resistance then follows from V and I as indicated in the figure above. Contact resistance at the current terminals stays outside the measurement, and although the contact resistance of the potential terminals remains in circuit, it forms a very small fraction of the high-resistance potential path and so causes negligible error.
The following methods are employed for measuring low resistances:
- Kelvin’s Double Bridge Method
- Potentiometer Method
- Ducter Ohmmeter
Kelvin’s Double Bridge
A Kelvin’s double bridge is a modification of the simple Wheatstone bridge. The figure below shows its circuit diagram.
As the figure shows, there are two sets of arms: one with resistances P and Q and the other with resistances p and q. R is the unknown low resistance and S is a standard resistance. Here r represents the contact resistance of the link between the unknown and standard resistances, whose effect we need to eliminate. For measurement the ratios are kept equal, P/Q = p/q, so a balanced Wheatstone bridge forms and the galvanometer shows null deflection. For a balanced bridge we can write
Substituting Equation 2 into Equation 1 and applying the ratio P/Q = p/q gives
The balance condition therefore does not contain r: balanced double arms remove the link resistance and the error due to it. To cancel another error caused by thermo-electric emf, one further reading is taken with the battery connections reversed, and the average of the two readings is used. This bridge suits resistances in the range 0.1µΩ to 1.0 Ω.
Ducter Ohmmeter
The Ducter Ohmmeter is an electromechanical instrument for measuring low resistances. It carries a permanent magnet like a PMMC instrument, with two coils mounted within that magnetic field at right angles to each other and free to rotate about a common axis. The diagram below shows a Ducter Ohmmeter and the connections needed to measure an unknown resistance R.
One coil, called the current coil, connects to current terminals C1 and C2; the other, called the voltage coil, connects to potential terminals V1 and V2. The voltage coil carries a current proportional to the voltage drop across R, so its torque follows that drop, while the current coil carries a current proportional to the current through R and produces a matching torque. The two torques act in opposite directions, and the pointer settles where they balance. This instrument covers resistances from about 100µΩ to 5 Ω.
Measurement of Medium Resistance (1Ω – 100kΩ)
The methods employed for measuring a resistance whose value lies in the range 1Ω to 100kΩ are:
- Ammeter-Voltmeter Method
- Wheatstone Bridge Method
- Substitution Method
- Carey-Foster Bridge Method
- Ohmmeter Method
Ammeter Voltmeter Method
This is the crudest yet simplest method of measuring resistance. It uses an ammeter to read current I and a voltmeter to read voltage V, giving the value of the resistance as
Two connections of ammeter and voltmeter are possible, shown in the figure below.
In figure 1 the voltmeter measures the drop across the ammeter plus the unknown resistance, hence
and the relative error is
In figure 2 the ammeter measures the sum of the currents through voltmeter and resistance, hence
and the relative error is
The relative error falls to zero for Ra = 0 in the first case and Rv = ∞ in the second. Which connection suits which case? Equating the two errors gives
Resistances above the value given by this equation suit the first connection; smaller ones suit the second.
Wheatstone Bridge Method
This is the simplest and most basic bridge circuit used in measurement studies. Its four arms carry resistances P, Q, R and S. R is the unknown resistance under test and S is a standard resistance; P and Q are known as the ratio arms. An EMF source connects between points a and b, and a galvanometer connects between points c and d.
A bridge always works on null detection: a parameter is varied until the detector reads zero, and the unknown is then computed from the remaining known values. Here S is varied until the galvanometer shows null deflection, meaning no current flows between c and d because both points sit at the same potential. Hence
Combining the two equations gives the familiar result:
Substitution Method
The figure below shows the circuit for measuring an unknown resistance R. Here S is a standard variable resistance and r is a regulating resistance.
With the switch first in position 1, r is adjusted until the ammeter reads a chosen current, and that reading is noted. The switch then moves to position 2 and S is varied until the ammeter repeats the same reading. The value of S at which the ammeter matches position 1 equals the unknown resistance R, provided the EMF source stayed constant throughout the experiment.
Measurement of High Resistance (>100kΩ)
The following methods serve for measuring high resistance values:
- Loss of Charge Method
- Megger
- Megohm bridge Method
- Direct Deflection Method
Such measurements draw very small currents, yet the high resistances involved mean sizeable voltages appear readily. Several extra problems follow:
- Electrostatic charges can get accumulated on measuring instruments
- Leakage current becomes comparable to measuring current and can cause error
- Insulation resistance is the most common quantity in this class; however a dielectric behaves as a resistor and capacitor in parallel, so while measuring the insulation resistance (I.R.) the current contains both components and the true resistance is not obtained directly. The capacitive component decays exponentially but takes a very long time to die away, so different values of I.R. appear at different times.
- Protection of delicate instruments from high fields.
To overcome the leakage-current and capacitive-current problem we use a guard circuit: it bypasses the leakage current around the ammeter so the true resistive current is measured. The figure below shows two connections of voltmeter and micro ammeter for measuring R, one without a guard circuit and one with.
In the first circuit the micro ammeter reads both capacitive and resistive current, biasing the value of R; in the second it reads only the resistive current.
Loss of Charge Method
This method uses the voltage equation of a discharging capacitor to find an unknown resistance R. The figure below shows the circuit diagram, and the governing equations are
That analysis assumes no leakage resistance of the capacitor. To account for leakage we use the circuit shown in the figure below, where R1 is the leakage resistance of C and R is the unknown resistance.
We repeat the procedure once with switch S1 closed and once with S1 open. The closed-switch case gives
and the open-switch case gives
Using R1 from the second result in the expression for R’ yields R.
Megohm Bridge Method
This method applies the Wheatstone bridge philosophy with slight modification. A high resistance is represented as in the figure below.
G is the guard terminal. The resistor can also be represented as in the adjoining figure, where RAG and RBG are the leakage resistances. The circuit for measurement appears in the figure below.
The measured value is actually the parallel combination of R and RAG, which causes only negligible error.
Megger
Megger is among the most widely used instruments of electrical engineers and serves almost exclusively for measuring insulation resistance. It consists of a generator, hand-driven in older models and electronic in modern ones. A separate article discusses the megger in detail.
