The advent of FETinput multimeters greatly reduced reading accuracy
errors due to not taking into account the impedance of devices being
measured. A certain amount of familiarity with how to interpret
the indication on a meter movement on analog meters is still required
based on the multiplier switch position and scale selected, but
for most users simply reading the number beneath the pointer  or
interpolating its position between two numbers  is good enough.
Mirrored scales take the some of guesswork out of that by reducing
parallax issues. Finally, digital multimeters (DMMs) hit the scene
and made slackers out of just about all of us when it comes to making
voltage, current, and resistance measurements. With few exceptions,
only production test, research, and metrology environments require
pulling out the meter specifications to determine precision and
accuracy numbers. Other than not exceeding the meter input limits,
making a good connection between the leads and the device under
test (DUT) is important for success. Purists and old codgers might
argue otherwise, but even they probably 'cheat' when nobody is looking
;)
Resistance Measurements
By Shepherd Litt, W2LCC
Superior Instruments Co.
Commercially constructed ohmmeter. This
instrument is highly portable and houses a precision standard
resistance which is used as a companion when measuring an
unknown resistance.

A review of the various methods used in the measurement of
resistance, from the simplest form to the more highly accurate laboratory
methods. Examples are presented whenever their use is justified
and formulas worked out so that anyone, with a small working knowledge
of mathematics, can make accurate measurements.
Accurate resistance measurements are an essential part of laboratory
procedure. For some types of work, an accuracy of ±2% is adequate,
while under other circumstances, much higher accuracy is necessary.
This article discusses several methods of resistance measurement
including the simple ohmmeter, the Wheatstone bridge, and the Kelvin
bridge.
Among the simplest methods that can be employed in the measurement
of resistance is the socalled ammeter method. This method, illustrated
in Fig. 1A, employs a source of potential, an ammeter or milliammeter,
and the unknown resistance.
Ohm's law states that R = E/I. Resistance is equal to the voltage
impressed across a circuit divided by the current flowing through
the circuit. If we employ a 1.5volt cell as a source of potential
and impress this voltage across an ammeter and unknown resistance
in series, and the ammeter reads 0.2 ampere, the circuit resistance
is 7.5 ohms. Note that 7.5 ohms is not the resistance of the unknown
resistance, but is the resistance of the entire circuit (unknown
resistance, ammeter, connecting wires and internal resistance of
the cell).
To determine the resistance of the resistor, it is necessary
to deduct the ohmage of the ammeter, wires, and internal resistance
of the cell from 7.5 ohm total. In order to obtain high accuracy
in this method, several points must be borne in mind.
1. Use a large cell having low internal resistance (a storage
battery is ideal).
2. Use largediameter connecting wires having low resistance.
3. Use an ammeter having a very low resistance.
4. Know the resistance of the ammeter.
5. Be sure that the ammeter is accurate.
For values of resistance above 10 times the resistance of the
ammeter, the ammeter resistance, the connecting wires, and the internal
resistance of the cell may be disregarded. The accuracy of the ammeter
method can be further increased by employing a standard resistor
and basing the calculations on this standard (Fig. 1B).
Assuming that the standard resistance is 10 ohms, then, with
the switch in position No.1 the ammeter reads 1 ampere. With the
switch in position No.2 the ammeter reads 0.25 ampere. Since the
amount of current passing through a resistance is inversely proportional
to its resistance, then
x : 10 = 4:1; or the resistance of the unknown is 4 times the
resistance of the standard, or 40 ohms.
Note that now only the resistance of the standard need be known.
Voltmeter Method
Fig. 1. (A) Diagram illustrates ammeter
method of measuring resistance. (B) Similar to that of (A)
with the exception that a standard resistance is used as
a comparison. (C) Diagram illustrates voltmeter method of
resistance measurement.
Fig. 2.  Commonly used ohmmeter. There
are two versions of this particular type: (A) Series type:
and (B) Shunt type.

Should no ammeter be available, a voltmeter may be used (Fig.
1C). If E_{1} is the impressed voltage read by the voltmeter,
and E_{2} the voltage read when the unknown resistance is
placed in series with the voltmeter, then
x resistance of meter = X_{R}
As an example, if the meter (having a resistance of 10,000 ohms)
in position 1 reads 6 volts (the battery voltage) and in position
2 reads 4 volts, then
or 5,000 ohms.
This is a very important formula and most commercial ohmmeters
use this principle.
The voltmeter method is simple and can be used to read higher
resistances than the ammeter method. The main disadvantage of the
voltmeter method is that the meter must be capable of close reading
and its resistance must be known.
The voltmeter method can also be used in conjunction with a standard
resistance to improve its accuracy. It will be described later on
under Laboratory Measurements, as it is capable of high precision.
Ohmmeter Method
The common ohmmeter is a variation of the voltmeter method. There
are two types of ohmmeters, the series type (Fig. 2A) and the shunt
type (Fig. 2B).
In the series type, a battery, a milliammeter, and a resistor
are connected in series with the unknown resistor. The resistor
is made variable so that the meter can be brought to full scale.
As such, the resistor and the meter constitute a voltmeter which
can be brought to full scale to correspond to the voltage of the
battery. The value of the resistance required can be computed by
Ohm's law.
If a 1ma. meter and a 4.5volt battery are used, the series
resistor would then be 4500 ohms.
This can be made up by using a 3000ohm resistor and a 1500or 2000ohm
adjustable control. With the unknown resistance terminals shorted,
the meter is made to read full scale by varying the adjustable control.
The unknown resistor is then put in the circuit and the reading
noted. If the unknown resistance were to be 4500 ohms, the total
resistance in the circuit would be 9000 ohms and the 1ma. meter
would become a 9volt voltmeter, Since a 4,5volt battery is being
used as a source of potential, the meter will read half scale. A
resistance lower than 4500 will cause the meter to read more than
half scale, while a resistance greater than 4500 ohms will cause
the meter to read less than half scale. Zero resistance, therefore,
will correspond to full scale and would appear to the right of the
meter scale. If a meter having a regular linear scale is used, the
scale can be changed to an ohmmeter scale by employing the following
formula:
x divisions on meter
when R_{1} = meter resistance (as a voltmeter), R_{2}
= unknown resistance.
Using the abovementioned meter and battery as an example, and
if the meter is a 1ma. type with 4500 ohms internal resistance
and with 50 divisions on the scale, and the battery is 4.5 volts,
a 4500ohm resistor would read:
or 25 divisions on the 50division scale.
A 10,000ohm resistor would read 16 divisions on the same scale,
and a 500 ohm resistor would, in like manner, read 45 divisions.
The above method is the method employed by the writer in calculating
the resistance scales for one manufacturer in the instrument field.
Fig. 3.  (A) Ohmmeter employing a zero
adjusting control that is placed in shunt with the meter.
(B) Commercialtype ohmmeter based on both the series and
shunt circuits.

In order to reduce the range of the meter, a shunt can be employed.
By using a shunt to change the aforementioned 1ma. meter to 10
ma. and reducing the series resistance to 450 ohms, a reduction
ratio of 10 is brought and the center of the resistance scale then
becomes 450 ohms. To increase the range of the ohmmeter, either
a 45volt battery and 45,000ohm resistor can be employed with the
1ma. meter, or the meter sensitivity can be increased 10 times
to 100 microamperes.
In the above ohmmeter, the resistor in series with the meter
acts as a "zero adjuster control" to compensate for battery voltage
changes. In multirange instruments, this "zero adjuster control"
must be made with a special taper so that it can be employed successfully
to vary the meter on all ranges. It is often better to place the
control across the meter and use a fixed series resistance. This
is advantageous because the control has a much better adjustment
in this position and the circuit can be proportional, so that no
adjustment need be made when changing ranges. Fig. 3A shows such
a circuit.
The low range of the instrument is 05000 ohms, with 35 ohms
center scale; and the high range is 0500,000 ohms, with 3500 ohms
center scale.
The series type of ohmmeter is the most common type of ohmmeter
in use today, its accuracy being normally 2% of the linear arc;
i.e., if the arc of the meter is 90°, then all readings are
accurate to 1:8° at any part of the scale.
Although the series ohmmeter is often used for low resistance
measurements, it has been deemed advisable to use another circuit
in place of it. Referring back to the circuit of Fig. 3A, the low
range consists of the 24 and 11ohm resistors in series with the
unknown and the 4.5volt battery. If the unknown resistance is 10
ohms, a total of 45 ohms is in series with the battery. Neglecting
the current used to actuate the meter, this means that a current
of 100 ma. is being taken from the battery, and if used continually
for low resistance testing, would exhaust the battery. To circumvent
this, the shunt ohmmeter is used.
The shunt type (Figure 2B) is the series ohmmeter with the leads
shorted and the resistance placed across the meter. The effect of
the resistance in this position is to act as a shunt across the
meter to reduce the scale reading. Since a short across the meter
will cause the meter not to read at all, the zero point corresponds
to the zero of a regular voltmeter, pointing to the left and the
"infinity" mark to the right.
The formula for calculating the shunt ohmmeter is exactly opposite
that for the series ohmmeter, and can be written:
x divisions of the meter scale.
Fig. 4.  Scale divisions of a commercially
built ohmmeter. Superior Instruments Company's model 1552.

Because of this fact, the resistance of the meter appears in
the center of the scale.
The shunt ohmmeter finds its chief use in measuring resistances
less than 100 ohms. If the meter is to measure resistances less
than 6 ohms, the length and resistance of the testleads must be
figured into the computation of the scale. A pair of commercial
testleads (36") has a resistance greater than 0.06 ohms. If the
resistance were not taken into account when the scale of the meter
was computed, an error of 1% would exist at the 6ohm point. The
error at 0.6 ohms would be 10%. If the resistance of the testleads
were added to the meter resistance, the error would be eliminated.
A typical commercial ohmmeter employing both series and shunt
circuit is diagrammed in Fig. 3B. This is a commercial ohmmeter
manufactured by Superior Instruments Company, their model 1552.
The scale of this instrument is shown in Fig. 4. The series ohmmeter
is used for the high range of 01000 ohms and the shunt ohmmeter
used for the low range 010 ohms. Note that the end of calibration
of the low resistance scale is not at the extreme left, but slightly
before the end of the scale. The zero point corresponds to the 0.06
ohm testleads used with this instrument. Some commercial instruments
omit the "zero adjuster" control by employing a magnetic shunt across
the meter. This has the effect of increasing or decreasing the sensitivity.
The above methods are commercial methods in use today and, unless
extreme precautions are taken, cannot successfully be used to measure
better than 2%. To achieve a higher degree of accuracy, laboratory
methods must be used. Two general methods are employed in the laboratory:
the potentiometer method and the bridge method.
In the potentiometric method, the voltage drop across the standard
resistance is compared to the voltage drop across the unknown. It
can best be described as the voltmeter method used with a standard
resistance. (A potentiometer is an instrument measuring voltage
below 1.6 volts, employing a null method. It is adjusted and calibrated
by means of a standard cell and has an accuracy of better that 0.05%.
Most laboratory potentiometers have an accuracy of 0.01% and 0.02%)
In the method employed, current is sent through both the standard
resistance, usually having an accuracy of 0.05 % or better, and
the unknown resistance. The voltage drop across the standard is
read first, and then the drop across the unknown, by means of the
potentiometer. If, for example, a standard resistance of 1 ohm is
used and the voltage drop across it is found to be 1 volt, with
the voltage drop across the unknown 1.016 volts, the unknown resistance
is 1.016 ohms. This is true since the same current that passed through
the two resistances makes their voltage drops proportionate to their
resistances.
A commercial instrument utilizing this principle, the model P25,
manufactured by Superior Instruments Company, operates on the following
principle: A current is sent through a precision standard resistance
and the unknown. The voltage drop across the standard is adjusted
until the meter reads full scale, by means of a control and a momentary
"standardizing" switch. When the switch is released the drop across
the unknown is read. Although the instrument really measures voltage
drops, the scale is calibrated in ohms. The indicating instrument
is a precision mirrorscale millivoltmeter, having 100 divisions.
Range of the instrument 0  0.005, 0  0.05, 0  0.5, since it was
made primarily to measure low resistances such as solid rods of
metals, switch contacts, etc. The lowest reading possible is 0.00005
ohms with the limit of error 1 division or 1% at any part of the
scale. Readings can be estimated to 1/4 division. Although this
instrument was made primarily to measure low resistances, it can
be converted to read high resistances by a small change in wiring.
It should be especially noted that the scale of this and similar
instruments operating on the same principle are linear, as compared
with the crowded scales of ordinary resistance meters.
The more common type of laboratory resistance meter is the bridge.
There are two basic types of bridges: the wheatstone bridge, for
measuring resistances above 0.1 ohm, and the Kelvin bridge, sometimes
called a double bridge, for measuring resistances below 1 ohm.
Wheatstone Bridge
A Wheatstone bridge (Fig. 5) is a closed resistance network of
four arms. Two of the arms (A and B) are ratio arms and are usually
fixed resistances. The C arm is a variable arm, usually fixed resistances
controlled by a switch and made so up to 1000 ohms in 0.1 ohm increments.
The X arm is the unknown resistance. A source of voltage is, in
most cases, applied between the B and C arms and the A and X arms.
A galvanometer, having high voltage sensitivity, is connected between
the junctions of the A and B arms and the C and X arms. Balance
of the bridge (no galvanometer reading) is had when:
The accuracy of commercial laboratory Wheatstone bridges runs
from 0.5 of 1% in portable models to 0.02 % in high precision models.
A variation of the Wheatstone bridge employs a slide wire in
place of fixed ratio arms and a fixed resistance standard in place
of the C arm. Although the accuracy of the slidewire bridge is
usually less than that of the fixedratio bridge, it has the advantage
of greater speed in reading.
Kelvin Bridge
Fig. 5.  Wheatstone bridge.
Fig. 6.  Kelvin bridge.

The Wheatstone bridge cannot be successfully used to measure low
resistances. If we take a bar of metal and try to measure its resistance
by means of a Wheatstone bridge, several important facts must be
borne in mind. The resistance of the connecting leads must be accurately
known, since they contribute to the resistance indicated by the
bridge. Resistance of the contacts between the bar and the connecting
wires must be known for the same reason. By employing large lowresistance
cable as connectors, the former can be deducted from the bridge
reading, but the latter (contact resistance) can never be accurately
known. Because of this fact, the Wheatstone bridge is never used
to measure below 0.1 ohm, although theoretically it is possible.
In the Kelvin bridge, the resistance of the connecting leads
and contacts are unimportant since they are put in series with the
comparatively highresistance ratio arms. This can be done only
by employing current and potential terminals for both the standard
and the unknown resistance. The resistance measured by the Kelvin
bridge is the resistance between the potential leads only. Fig.
6 illustrates the operation of the Kelvin bridge.
A and B: The regular ratio arms similar to those employed in
a Wheatstone bridge.
a and b: A duplicate set of ratio arms.
Yoke: This is the connecting bar between the standard and the
unknown. Note that a and b shunt the yoke and therefore its resistance
does not enter into the calculation.
C and C: The current connections of the standard resistance.
C' and C': The current connections of the unknown.
P and P: The potential leads of the standard.
P' and P': The potential leads of the unknown.
G: The galvanometer that is used to indicate when the bridge
is balanced.
Since all the heavy current goes through the current terminals
(there is only a low circulating current flowing through the ratio
arms) the contact resistance of the potential leads has no effect
on the measured resistance. A commercial laboratory version of a
high precision Kelvin bridge is that manufactured by the Leeds &
Northrup Company and comprises two units, the 4320 dual ratio box
and the 4300 low resistance standard.
The dual ratio is made up of 10 resistors, two each of 1003004001000
and 10,000 ohms. These coils are adjusted to better than 0.05 %
of their nominal value. They are controlled by plugs and give ratios
of 100, 10, 1, 0.1, and 0.01 of the standard. Other ratios can be
had by inserting the plugs into other combinations of jacks. Since
the lowest ratio arm resistance is 100 ohms, contact and lead resistance
can be as high as 0.01 before an error of 0.01% is had from this
source. In practice, contact and lead resistance is much less than
0.01 ohm.
In this case, the standard resistance consists of nine coils,
each 0.001 ohm, plus a calibrated bar 0.0011. These resistances
are accurate to 0.02%. The nine coils in conjunction with the calibrated
bar have the effect of a bar 10 times as long. Nine coils can carry
a current of 50 amperes continuously and the bar alone can carry
150 amperes. The bar is calibrated to 100 divisions, and a vernier
screw allows readings down to 0.1 division. Range of this Kelvin
bridge is from 0.000,000,011 to 1 ohm, with an accuracy of 0.04%.
A portable Kelvin bridge is diagrammed in Fig. 7. This is the
Leeds & Northrup type 4286 Kelvin bridge ohmmeter. The portable
bridge compares the unknown resistance against 5 standard resistances
by means of a dual ratio arm that is variable. Resistance of the
unknown is equal to the dial setting of the ratio arms multiplied
by the standard in use, with the dial calibrated 0.01 to 0.11 ohms.
The range of the portable bridge is from 0.0001 ohm to 11 ohms,
and the error is less than 2% of the setting.
Special Circuits
Fig.7.  Diagram of Leeds & Northrup
portable type 4286 Kelvin bridge ohmmeter.

Besides the above mentioned methods, special circuits are sometimes
used:
The No.1 Weston ohmmeter uses a D'Arsonval movement, but with
a tapped coil. The current through one coil remains constant, while
the current through the second section varies with the resistance
connected across the meter terminals. Its coils are so wound that
when no resistance is in the circuit, the torque of the two coils
are equal and the meter reads zero. When a resistance is inserted
in the circuit, the current in the "resistance" coil only partially
nullifies the current of the "current" coil, causing the meter to
read up scale. Provisions are made for adjusting the meter by means
of a magnetic shunt to compensate for aging of the battery. A mirror
scale is provided and the scale is very close to linear.
The megger is an instrument, formerly made in England but since
the war manufactured in the United States, that is used primarily
to measure insulation resistance. The instrument consists of a dual
(current and voltage) coil, shaped like a T, rotating in the field
of a permanent magnet. No springs are used in the instrument. The
magnet also supplies the field for a small d.c. generator with a
potential of 500 volts, which is operated by rotating a hand crank.
In operation the crank is rotated and the 500 volts generated is
applied to the voltage coil, turning the coil so that the pointer
appears at the "infinity" mark on the scale. 500 volts is also applied
to the resistance (insulation) through the current coil. The torque
produced by the current passing through the current coil and the
insulation resistance, opposes the torque of the voltage coil, causing
the pointer to swing away from the infinity mark to a point on the
scale corresponding to the resistance being measured. A "megger"
finds its chief use in measuring insulation resistance where a source
of power cannot be had. The range of this instrument is usually
100 megohms and 500 volts. Special instruments can be had to measure
resistance up to 20,000 megohms at a test potential of 2500 volts.
A special resistance meter recently designed by the writer is
worth describing. It operates on the bridge principle, but in place
of a null indicating meter, the meter is calibrated from 1 to 10.
The range of the instrument is from 0.1 ohm to 10 megohms in decade
steps  i.e., 0.1 ohm to 1 ohm, 1 to 10 ohms, 10 ohms to 100 ohms,
etc. With a meter scale of 90 divisions, each division represents
1% of full scale. The meter can be read with ease to 1/4 division
or 25% of full scale. The meter has been built in several ways.
It has been used as a limit bridge, a temperature bridge, and a
resistance meter. As a limit bridge it has been made as sensitive
as ± 0.1% of the standard in use. As a resistance meter it has replaced
a regular bridge, since it is speedier in operation; resistances
are measured as quickly as in a conventional ohmmeter, but with
the accuracy of a bridge.
Methods other than outlined above have been occasionally used
in resistance measurements. However, they are not as common and
are seldom used.
Posted May 1, 2015
