SME
Measurements & Instrumentation
Strain, temperature and pressure measurement
Use this for “A 120 Ω gauge with GF = 2.1 sees 500 microstrain in a quarter bridge at 5 V. Find ΔR and the bridge output.”
Diagram
Vₒᵤₜ
=
Vₑₓ
×
GF
×
ε
4
Vₒᵤₜ
=
5
V
×
2.1
×
500
με
4
=
1.313
mV
One gauge stretched: its R rises by ΔR = GF × ε × R and the bridge leaves balance.
Resistance change ΔR = 0.126 Ω
This is an example. Type your own values to start a new problem.
ΔR (Ω)
R (Ω)
=
GF
×
ε (με)
Vₒ (mV)
=
Vₑₓ (V)
×
×
ε (με)
4
ε is in microstrain (1 με = 10⁻⁶) and Vₒ in mV: that is where the formulas’ ÷ 1,000,000 and ÷ 4000 come from.
Formulas
ΔR
=
GF
×
ε
×
R
1,000,000
0.126
=
2.1
×
500
×
120
1,000,000
Vₒ
=
Vₑₓ
×
GF
×
ε
4,000
1.3125
=
5
×
2.1
×
500
4,000
Assumptions
•
The bridge starts balanced, with three fixed arms equal to the unstrained gauge.
•
The strain is small, so Vₒ = Vₑₓ GF ε ÷ 4 holds; its error is about GF ε ÷ 2 of Vₒ.
•
Temperature changes are compensated (a dummy gauge or a self-compensated gauge).
Step-by-step
WE KNOW
ε = 500 με, GF = 2.1, R = 120 Ω, Vₑₓ = 5 V
FIND
resistance change (ΔR), bridge output (Vₒ)
Step 1 · Find resistance change (ΔR)
Use ΔR = GF × ε × R ÷ 1,000,000
The
gauge’s
resistance
changes
by
GF
times
the
strain,
as
a
share
of
R
;
÷
1,000,000
turns
με
into
strain.
ΔR
=
2.1
×
500
×
120
1,000,000
ΔR
=
1,050
×
120
1,000,000
ΔR
=
126,000
1,000,000
ΔR = 0.126 Ω
Step 2 · Find bridge output (Vₒ)
Use Vₒ = Vₑₓ × GF × ε ÷ 4,000
One
arm
of
four
changes
by
GF
×
ε
,
so
the
meter
sees
a
quarter
of
that
times
Vₑₓ;
με
times
V
gives
μV,
and
1000
gives
mV.
Vₒ
=
5
×
2.1
×
500
4,000
Vₒ
=
10.5
×
500
4,000
Vₒ
=
5,250
4,000
Vₒ = 1.3125 mV
Check
Put the numbers back in. Both sides should match.
0.126
=
2.1
×
500
×
120
1,000,000
✓
1.3125
=
5
×
2.1
×
500
4,000
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Thermocouple with a reference junction
Use this for “A type K thermocouple (about 41 μV/°C) has its reference at 25 °C and its tip at 250 °C. What voltage does it make?”
A 4–20 mA pressure transmitter
Use this for “A transmitter spans 200 to 1000 kPa on 4–20 mA. What current at 350 kPa, and what pressure gives 12.8 mA?”