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February 1959 Popular Electronics
 Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
Popular Electronics,
published October 1954 - April 1985. All copyrights are hereby acknowledged.
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The Wheatstone
bridge is a fundamental electronic circuit invented by Charles Wheatstone in
1843, renowned for its exceptional precision in measuring unknown electrical
resistances. Its basic configuration consists of four resistors arranged in a
diamond pattern with a voltage source and a zero-center galvanometer. When the
bridge is "balanced" and the galvanometer reads zero, the ratio of the
resistances is equal, allowing the value of an unknown resistor (Rx) to be
calculated using the formula Rx = R2 × (R3/R4). This Popular Electronics
magazine article explains how to construct a simple, accurate bridge using a
slide wire for R3 and R4, where their ratio is determined by the lengths of the
wire. By selecting a known resistor for R2 and adjusting the slide until balance
is achieved, one can precisely calculate Rx. Beyond resistance, the principle is
widely adapted for measuring capacitance, inductance, and in various control and
testing applications, making it one of electronics' most versatile circuits.
After Class: The Wheatstone Bridge
 By Harvey Pollack
Aside from the simple series and parallel circuits, the Wheatstone bridge arrangement
probably appears in more electronic applications than any other circuit. Invented
in 1843 by the English scientist, Charles Wheatstone, the original bridge has been
modified countless times to make it suitable for thousands of different uses in
control circuits, testing, and radio and television.
Just what is a Wheatstone bridge? What principles are involved in its operation?
What is it used for?
Operating Principle
The fundamental bridge circuit is given in Fig. 1. The arrangement comprises
Rx and R2 in series, R3 and R4 in series,
with the two series groups in parallel with each other across the voltage source.
A zero-center galvanometer (M1) is connected to junctions B and D.
By correctly selecting the four resistance values, it is possible to make the
galvanometer read zero regardless of the voltage of the battery (B1). When the galvanometer
reads zero, the voltage across points B and D must also be zero. There is only one
way that this can happen:
(a) The voltage drop across Rx (from A to B) must equal the voltage
drop across R3 (from A to D). Designating the current in the upper series
branch (A-B-C) as I1 and the current in the lower series branch (A-D-C)
as I2, we can write: I1 x Rx = I2 x
R3 since a voltage drop is always the product of the current times the
resistance.
Fig. 1 - Basic Wheatstone bridge circuit from which all the other
bridge circuits are derived.
(b) Since the voltage across both branches must be equal to the battery potential
applied across A-C, then from condition (a) we know that the drop across R2
must equal the drop across R4. The current in R2 is I1
since R2 and Rx are in series. Similarly, the current in R4
is I2. Thus:
I1 x R2 =I2 x R4
(c) If the first equation is divided by the second, all the currents cancel out
and we are left with the simple relation:
Rx/R2 = R3/R4
If we now multiply both sides of this last equation by R2, we arrive at the final
form:
Rx = R2 x (R3/R4)
What this final equation really says is that the value of an unknown resistance
Rx may be obtained if the other three resistances are known. Using the correct value
of Rx, the bridge can be "balanced," that is, the galvanometer will show no deflection.
Measurement of resistances on the Wheatstone bridge can be extremely accurate -
much more so than by VOM or VTVM.
Building Your Own Bridge
An amazingly precise Wheatstone bridge can be constructed in an hour or two from
some inexpensive materials and any zero-centered sensitive meter. (Many of the surplus
mail order houses can supply inexpensive microammeters of this type.) The construction
details are illustrated in Fig. 2.
A slide wire consisting of about three feet of #28 nichrome or similar material
taken from an old wire-wound rheostat forms R3 and R4. A test
probe can be slid along the Nichrome wire so that R3 measured from A
to D is varied as R4 (D to C) is simultaneously changed in the opposite
sense.
The actual resistance of R3 and R4 need not be known. Since
resistance of a uniform wire varies directly as the length, the ratio of the length
AD to the length DC as read on the yardstick or meter stick is the same as R3/R4.
Hence, all you have to know accurately is the resistance of R2.
You might build up a supply of 1% resistors of different values for substitution
across the R2 binding posts, or if you own a resistance decade box, this can be
used.
Commercial bridge instrument for resistance and capacity measurements
available in kit form
(Paco C-20).
Fig. 2 - Details of homemade slide-wire Wheatstone bridge.
Using the Bridge
Suppose you want to find the resistance of an unknown resistor with good precision.
If you know the approximate range of resistance that you're dealing with, choose
a value for R2 of about the same range. If you have no idea of the value
of Rx, use a hit-or-miss system.
Precision resistor decade box of the type used to provide a resistance
standard (Eico 1171).
Touch the test prod to the slide wire near the center and, making sure that the
protective resistor switch is open, tap the key while you watch the meter. The deflection
will probably be large. Now slide the prod along the wire in the direction that
causes the deflection to decrease. If you have to go to either end of the slide
wire before reaching zero, R2 has been incorrectly selected - try another
value.
When you finally obtain a zero reading with the test prod at least 3" away from
an end of the wire, close the knife switch (this short-circuits the protective resistor)
and again tap the key. The instrument will now be very sensitive, so inch your way
along the wire until you again obtain zero deflection. Note the length AD (R3)
and DC (R4) on the yardstick; then merely substitute in the last equation
and solve for the value of Rx.
For example, let's say that an unknown resistor of about 10,000 ohms is to be
measured. R2 is chosen as 10,000 ohms (1%) and the slide-wire bridge
manipulated until the galvanometer shows balance. Length AD turns out to be 46.4
centimeters on the meter stick. Hence, length DC must be 53.6 cm. since one meter
contains 100 cm. Thus:
Rx = R2 x R3/R4
Rx = 10,000 x 46.4/53.6
Rx = 8660 ohms ± 1%
The Wheatstone bridge principle is not limited to simple resistance measurements.
In modified form, it can be used for determining unknown capacitances and inductances,
for measuring gain of electron tubes (in the form of a Miller bridge), detection
of leakage in insulation, and many other important applications. A modified Wheatstone
bridge, the series resistance-capacitance bridge, will be described in After Class
in the March issue.
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