Physics 3330
Experiment #2
Fall 2009
DC Measurements, Voltage Dividers, and Bridges
Purpose
You will gain familiarity with the circuit board and work with a variety of DC techniques,
including the Wheatstone bridge and the 4terminal resistance measurement techniques.
Reading:
H&H Section 1.03, 1.04, 1.05.
Theory
1. The Basic Wheatstone Bridge
Bridge circuits are used to precisely compare an unknown impedance with a standard.
The
simplest example is the Wheatstone bridge (Fig. 2.1), a fourarm bridge with a resistor in each
arm, which is usually used at DC or low frequencies.
It has many applications in measurement
circuits, where often the unknown resistance R
x
is a resistive sensor, such as a platinum
thermometer or a mechanical strain gauge (see H&H 15.03).
There are other types of bridges,
including AC bridges with capacitors or inductors in one or more arms, radiofrequency bridges,
and bridges that use precision transformers to generate voltage ratios.
In our the basic bridge R
x
, R
s
, R
1
, & R
2
are each >>0.1
Ω
so that all contact resistances
(typically of order .1
Ω
) can be ignored.
The bridge is made from two voltage dividers, each
connected to the same source voltage
ε
.
When the division of the two dividers is adjusted to the
same value the null meter reads zero voltage (
∆
V=0).
This occurs when R
x
/R
s
= R
1
/R
2
, a
formula which can solved for the unknown resistor R
x
in terms of the standard R
s
and the ratio
R
1
/R
2
.
Fig. 2.1
a) Basic Wheatstone bridge.
b) Thevinin equivalent circuit.
(b)
A
B
ε
_
+
Τ
R
T
∆
V
}
2
=10k
Ω
=SR
P
=(1S)R
P
R
x
Nullmeter
R
S
ε
+
_
Voltage
Source
}
R
10turn potentiometer
R
P
R
1
Standard
Unknown
B
∆
V
(a)
A
Experiment #2
2.1
Fall 2009
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More generally, the operation of the bridge, both in the balanced and the unbalanced states,
follows directly from its Thévenin equivalent and the equations:
.
,
2
1
2
1
2
1
1
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
s
x
x
s
T
s
x
x
T
+
+
+
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
−
+
=
ε
ε
Stare at these equations for a while and try to see why they are correct without doing any
calculations.
2.
Fourterminal Connections
Typically, when we wish to measure the resistance of a circuit element we can simply connect
the element between the two leads of a DMM and read “Ohms”.
With the modern digital DMM
this works quite well unless the resistance of the element to be measured is small  not very
much higher than the resistances of the leads or contact resistances between the sample and the
leads (probably less than an ohm for your leads).
If the element’s resistance is not much higher
than the leads, then the lead resistance will make a sizeable impact on the measurement, skewing
it badly.
The way around this is to use the method of 4terminal connections, in which the
current leads are separate from the voltage leads. A schematic is shown in Figure 2.2.
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 '09
 Resistance, Work, Heat, Alternating Current, Direct Current, Voltage divider, power supply, Electrical resistance

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