How to Calculate and Solve for Resistance of a Strain Gauge Wire | Instrumentation

January 21, 2021April 24, 2024 Loveth Idoko

Last Updated on April 24, 2024

The image above represents the resistance of a strain gauge wire. To calculate the resistance of a strain gauge wire, four essential parameters are needed, and these parameters are the Resistivity of the Strain Gauge Wire (ρ), Length of the Strain Gauge Wire (L), Wire Constant (k) and Diameter of Wire (D).

The formula for calculating the resistance of a strain gauge wire:

R = ^ρL / _kD²

Where:

R = Resistance of a Strain Gauge Wire
ρ = Resistivity of the Strain Gauge Wire
L = Length of the Strain Gauge Wire
k = Wire Constant
D = Diameter of Wire

Let’s solve an example;
Find the resistance of a strain gauge wire when the resistivity of the strain gauge wire is 8, the length of the strain gauge wire is 2, the wire constant is 4, and the diameter of the wire is 6.

This implies that;

ρ = Resistivity of the Strain Gauge Wire = 8
L = Length of the Strain Gauge Wire = 2
k = Wire Constant = 4
D = Diameter of Wire = 6

R = ^ρL / _kD²
R = ^{8 x 2} / _{4 x 6²}
So, R = ¹⁶ / _{4 x 36}
R = ¹⁶ / ₁₄₄
R = 0.11

Therefore, the resistance of the strain gauge wire is 0.11 Ω.

Calculating for the Resistivity of the Strain Gauge Wire when the Resistance of a Strain Gauge Wire, the Length of the Strain Gauge Wire, the Wire Constant and the Diameter of Wire is Given

ρ = R x kD²

Where;

ρ = Resistivity of the Strain Gauge Wire
R = Resistance of a Strain Gauge Wire
L = Length of the Strain Gauge Wire
k = Wire Constant
D = Diameter of Wire

Let’s solve an example;
Find the resistivity of the strain gauge wire when the resistance of a strain gauge wire is 12, the length of the strain gauge wire is 8, the wire constant is 10, and the diameter of the wire is 4.

This implies that;

R = Resistance of a Strain Gauge Wire = 12
L = Length of the Strain Gauge Wire = 8
k = Wire Constant = 10
D = Diameter of Wire = 4

ρ = R x kD²
Then, ρ = 12 x (10)4²
ρ = 12 x 160
ρ = 1920

Therefore, the resistivity of the strain gauge wire is 1920.

Calculating the Length of the Strain Gauge Wire when the Resistance of a Strain Gauge Wire, the Resistivity of the Strain Gauge Wire, the Wire Constant and the Diameter of the Wire are Given

L = ^{R x KD²} / _ρ

Where;

L = Length of the Strain Gauge Wire
R = Resistance of a Strain Gauge Wire
ρ = Resistivity of the Strain Gauge Wire
k = Wire Constant
D = Diameter of Wire

Let’s solve an example;
Find the length of the strain gauge wire when the resistance of a straining wire is 10, the resistivity of the strain gauge wire is 8, the wire constant is 5, and the diameter of the wire is 2.

This implies that;

R = Resistance of a Strain Gauge Wire = 10
ρ = Resistivity of the Strain Gauge Wire = 8
k = Wire Constant = 5
D = Diameter of Wire = 2

L = ^{R x KD²} / _ρ
L = ^{10 x (5)(2²)} / ₈
So, L = ^{10 x 25} / ₈
L = ²⁵⁰ / ₈
L = 31.25

Therefore, the length of the strain gauge wire is 31.25.

Calculate the Wire Constant when the Resistance of a Strain Gauge Wire, the Resistivity of the Strain Gauge Wire, the Length of the Strain Gauge Wire and the Diameter of Wire is Given

K = ^ρL / _{R x D²}

Where;

k = Wire Constant
R = Resistance of a Strain Gauge Wire
ρ = Resistivity of the Strain Gauge Wire
L = Length of the Strain Gauge Wire
D = Diameter of Wire

Let’s solve an example;
Find the wire constant when the resistance of a strain gauge wire is 20, the resistivity of the strain gauge wire is 14, the length of the strain gauge wire is 11, and the diameter of the wire is 4.

This implies that;

R = Resistance of a Strain Gauge Wire = 20
ρ = Resistivity of the Strain Gauge Wire = 14
L = Length of the Strain Gauge Wire = 11
D = Diameter of Wire = 4

K = ^ρL / _{R x D²}
That is, K = ^{14 x 11} / _{20 x 4²}
K = ¹⁵⁴ / ₃₂₀
K = 0.48

Therefore, the wire constant is 0.48.

Calculate the Diameter of Wire when the Resistance of a Strain Gauge Wire, the Resistivity of the Strain Gauge Wire, the Length of the Strain Gauge Wire and the Wire Constant are Given

D = √^ρL / _{R x K}

Where;

D = Diameter of Wire
R = Resistance of a Strain Gauge Wire
ρ = Resistivity of the Strain Gauge Wire
L = Length of the Strain Gauge Wire
k = Wire Constant

Let’s solve an example;
Find the diameter of the wire when the resistance of a strain gauge wire is 16, the resistivity of the strain gauge wire is 12, the length of the strain gauge wire is 10, and the wire constant is 13.

This implies that;

R = Resistance of a Strain Gauge Wire = 16
ρ = Resistivity of the Strain Gauge Wire = 12
L = Length of the Strain Gauge Wire = 10
k = Wire Constant = 13

D = √^ρL / _{R x K}
D = √^(12)(10) / _{16 x 13}
Then, D = √¹²⁰ / ₂₀₈
D = √0.576
D = 0.758

Therefore, the diameter of wire is 0.758.

How to Calculate and Solve for Resistance of a Strain Guage Wire With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the resistance of a strain gauge wire.

To get the answer and workings of the resistance of a strain gauge wire using the Nickzom Calculator – The Calculator Encyclopedia, first, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on instrumentation under Materials and Metallurgical

Now, Click on Resistance of a Strain Gauge Wire under Instrumentation

The screenshot below displays the page or activity to enter your values, to get the answer for the resistance of a strain gauge wire according to the respective parameters which is the Resistivity of the Strain Gauge Wire (ρ), Length of the Strain Gauge Wire (L), Wire Constant (k) and Diameter of Wire (D).

Now, enter the values appropriately and accordingly for the parameters as required by the Resistivity of the Strain Gauge Wire (ρ) is 8, Length of the Strain Gauge Wire (L) is 2, Wire Constant (k) is 4 and Diameter of Wire (D) is 6.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia can calculate the resistance of a strain gauge wire and also presents the formula, workings and steps, too.