ENGINEERING-43
Wheatstone Bridge
Lab-05
Lab Data Sheet – ENGR-43 Lab-05
Lab Logistics
Experimenter: Bruce Mayer, PE
Recorder:
Date: 06Jan2011
Equipment Used (maker, model, and serial no. if available)
Directions
1. Note that in this and ALL OTHER Laboratory Exercises ENGINEERING UNITS must
accompany ALL Data-Entries and Calculated-Quantities
2. Check out a DMM and Power/Probe Leads for the Power-Supply and DMM
3. Go to the side counter, collect resistors, “bread board”, and leads required to construct the
circuit shown in Figure 1.
4. Make the Measurements and Calculations needed to complete all Data/Calculations tables.
 Note that when making potential measurements the POLARITY of the measurements is
very important to obtain the correct positive/negative SIGN in subsequent calculations
5. Return all lab hardware to the “as-found” condition
The Wheatstone Bridge Circuit
Due to their outstanding output-voltage sensitivity to changes in the component values,
Wheatstone Bridge Circuits i are very advantageous for the measurement of resistance,
© Bruce Mayer, PE • Chabot College • 291199289 • Page 1
inductance, and capacitance. Wheatstone bridges are widely used for strain measurements. A
resistor-based Wheatstone bridge is shown in Figure 1.
The circuit consists of 4 resistors arranged in a diamond orientation. An input DC voltage, or
excitation voltage, is applied between the top and bottom of the diamond and the output
voltage is measured across the middle. When the output voltage, VAB = VA – VB, is zero, the
bridge is said to be balanced. One or more of the legs of the bridge may be a resistive
transducer, such as a strain gage. The other legs of the bridge are simply completion resistors
with resistance equal to that of the unknown resistance (such as strain gages). As the
resistance of one of the legs changes, by a change in strain from a resistive strain gage for
example, the previously balanced bridge is now unbalanced. This unbalance causes a voltage
to appear across the middle of the bridge. This induced voltage may be measured with a
voltmeter or the resistor in the opposite leg may be adjusted to rebalance the bridge. In either
case the change in resistance that caused the induced voltage may be measured and
converted to obtain the engineering units appropriate to the variable-resistance transducer.
For the circuit of Figure 1 the output, VAB, may be calculated by
 R2
R4 
VAB  VA  VB  VS 


R

R
R3  R4 
2
 1
Equation 1
Then the %-UnBalanced
UB%  100 VAB VS
© Bruce Mayer, PE • Chabot College • 291199289 • Page 2
Equation 2
R1
+
-
Vs
R3
A
R2
B
R4
Figure 1 • The Wheatstone Bridge. Vs = 12.00 Vdc. R1 = R3 = 1-3 kΩ. R2 = R4 = 2-6 kΩ.
R1 and R3 Must have the SAME nominal value. R2 and R4 Must have the SAME nominal
Value. The R2:R1 resistance ratio must be >1.4:1
Table I – Actual Values as measured with DMM set to the highest-sensitivity range
 COLOR-CODED Resistor Values & Tolerances
R1 =
R2 =
R3 =
R4 =
 Actual (DMM) Values
Vs =
R1 =
R2 =
R3 =
R4 =
© Bruce Mayer, PE • Chabot College • 291199289 • Page 3
After constructing the circuit and making the measurement to complete Table I, make the
measurements and calculations need to complete Table II below.
Table II – Potential Measurements and Calculations
Value Determination
VA
VB
VAB
%-Unbalanced
Calculated
Measured
Now Swap the position of the R1-R3 and R2-R4 resistor pairs; i.e., the resistors that were on
the bottom of the diamond are moved to the top, and vice-versa. Again perform the
calculations and measurements
Table III – Potential Measurements and Calculations
Value Determination
VA
VB
VAB
%-Unbalanced
Calculated
Measured
Next consider this hypothetical circumstance. You have just completed the balance
measurements in Table II and Table III. Just then the OHM-meter function on the DMM fails.
You need to measure the resistance of a resistor with the SAME COLOR-CODE as R4 in
Figure 1.Call this new resistor Rx. Replacing R4 with Rx creates the “Quarter Bridge i” circuit
shown in Figure 2.
Since the VOLTAGE function of the DMM still operates, the value of VAB by Rx is easily
measured. Also, Isolating R4 in Equation 1, then replacing R4 with Rx yields:
 R2
V 
R3 
 AB 
R  R2 VS 
Rx   1
V
R2
1  AB 
VS R1  R2
ii
This circuit is called a QUARTER bridge because ¼ of the components has an Unknown value.
© Bruce Mayer, PE • Chabot College • 291199289 • Page 4
Equation 3
After replacing R4 with Rx, measure the new value of VAB. Use this new VAB value, call it VABx,
and DMM measured values from Table I to calculate the resistance value for Rx.
Also, since the DMM is actually NOT faulty measure the value of Rx using the Ohm-meter
function. Compare the two values of Rx by calculating the Δ% using the DMM value as the
baseline:
Rx % 
Rx ,CALC  R x , DMM
R x , DMM

100%
1
Equation 4
R1
+
-
Vs
R3
A
R2
B
Rx
Figure 2 • The Wheatstone Bridge in the ¼-Bridge configuration with Vs, R1, R2, and R3
unchanged from Figure 1 (UNswap the Resistors). Rx is a NEW resistor with the SAME
COLOR-CODE as the original R4
© Bruce Mayer, PE • Chabot College • 291199289 • Page 5
Table IV – Rx Determination by ¼-Bridge Voltage Measurement
VABx (Measured)
Rx,CALC
Rx,DMM
RxΔ%
Thus we see that the ¼-Bridge Wheatstone circuit can be used to determine a resistance if we
can measure the voltage difference. In this situation we independently measure V AB to then
find the dependent quantity, Rx. For this circumstance define the resistance measurement
sensitivity, Jii, of the ¼-Bridge circuit as:
J Vs , R1 , R 2 , R 3  
dRx
dVAB
Equation 5
Vs , R1 , R 2 , R 3
Approximate J for the circuit of Figure 1 using the data from Table I and Table IV as:
Rx , DMM  R4, DMM
dRx
Rx
J


 J
dVAB VAB
VABx  V AB4
Equation 6
Next, replace in Equation 1 R4 with Rx, and then take the derivative to find
dRx
dV AB
2

R3  Rx 

V s , R1 , R 2 , R 3
Vs R3
 Jd
Equation 7
Use the previous DMM measurements for Vs, R1, R2, R3, R4 and Rx to calculate J Δ and Jd
per Equation 6 and Equation 7.
Finally, compare the two values of J by calculating the Δ% using the EXACT (calculus) value
as the baseline:
ii
The units for the resistance measurement sensitivity are inverse-Amps, which does not have a standard symbol,
so we’ll use “J”
© Bruce Mayer, PE • Chabot College • 291199289 • Page 6
J% 
J   J d 100%

Jd
1
Equation 8
Complete Table V. Be sure to include proper units
Table V – Resistance measurement sensitivity
JΔ
Jd
EXTRA CREDIT – 2 Lab-Points
Derive the bridge output equation shown in Equation 1
 Start with Diagram of Figure 1
 Derivation must proceed in a logical, step-by-step fashion
© Bruce Mayer, PE • Chabot College • 291199289 • Page 7
JΔ%
© Bruce Mayer, PE • Chabot College • 291199289 • Page 8
EXTRA CREDIT – 4 Lab-Points
Derive the sensitivity equation shown in Equation 7Equation 1
 Start with Equation 1, with R4 replaced by Rx
 Derivation must proceed in a logical, step-by-step fashion
© Bruce Mayer, PE • Chabot College • 291199289 • Page 9
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© Bruce Mayer, PE • Chabot College • 291199289 • Page 11
Print Date/Time = 29-May-16/03:59
© Bruce Mayer, PE • Chabot College • 291199289 • Page 12