Principle of Strain Gauge

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PRINCIPLE OF OPERATION
2.1 Principle of Strain Gauges
If external tensile force or compressive force increases or decreases the resistance proportionally increases or decreases. Suppose that original resistance R changes by ΔR because of strain ε, the following equation is set up.
            △R/R= Ks.ε
Where, Ks is a gauge factor, expressing the sensitivity coefficient of strain gages. General-purpose strain gauges use copper-nickel or nickel-chrome alloy for the resistive elements and the gage factor provided by these alloys is approximately 2.

2.2 Wheatstone Bridge
A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. The primary benefit of a Wheatstone bridge is its ability to provide extremely accurate measurements (in contrast with something like a simple voltage divider).  Its operation is similar to the original potentiometer.
The Wheatstone bridge was invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. One of the Wheatstone bridge's initial uses was for the purpose of soils analysis and comparison



Fig: 2.1 Wheatstone bridge
4.3 Operation
A Wheatstone bridge is widely used to measure the electrical resistance. This circuit is built with two known resistors, one unknown resistor and one variable resistor connected in the form of bridge. When the variable resistor is adjusted, then the current in the galvanometer becomes zero, the ratio of two unknown resistors is equal to the ratio of value of unknown resistance and adjusted value of variable resistance. By using a Wheatstone bridge the unknown electrical resistance value can easily measure.

4.4 Wheatstone bridge Circuit Arrangement

The circuit arrangement of the Wheatstone bridge is shown below.  This circuit is designed with four arms, namely AB, BC, CD & AD and consists of electrical resistance P, Q, R and S.  Among these four resistances, P and Q are known fixed electrical resistances. A galvanometer is connected between the B & D terminals via an S1 switch. The voltage source is connected to the A &C terminals via a switch S2. A variable resistor ‘S’ is connected between the terminals C & D. The potential at terminal D varies when the value of the variable resistor adjusts. For instance, currents I1 and I2 are flowing through the points ADC and ABC. When the resistance value of arm CD varies, then the I2 current will also vary.

                                    
Fig: 4.2 Wheatstone bridge Circuit Arrangement
If we tend to adjust the variable resistance one state of affairs could return once when the voltage drop across the resistor S that is I2. S becomes specifically capable to the voltage drop across resistor Q i.e. I1.Q. Thus the potential of the point B becomes equal to the potential of the  point D hence the potential difference b/n these two points is zero hence current through galvanometer is zero. Then the deflection in the galvanometer is zero when the S2 switch is closed.
4.5 Wheatstone bridge Derivation
From the above circuit, currents I1 and I2 are
                        I1=V/P+Q and I2=V/R+S
Now potential of point B with respect to point C is the voltage drop across the Q transistor, then the equation is
                I1Q= VQ/P+Q …………………………..(1)
Potential of point D with respect to C is the voltage drop across the resistor S, then the equation is
                 I2S=VS/R+S …………………………..(2)
From the above equation 1 and 2 we get,
                                   VQ/P+Q = VS/R+S
`                                 Q/P+Q = S/R+S
                                    P+Q/Q=R+S/S
                                       P/Q+1=R/S+1
                                              P/Q=R/S
                                               R=SxP/Q
Here in the above equation, the value of P/Q and S are known. So, R value can easily be determined. The electrical resistances of Wheatstone bridge such as P and Q are made of definite ratio, they are 1:1; 10:1 (or) 100:1 known as ratio arms and the rheostat arm S is made always variable from 1-1,000 ohms or from 1-10,000 ohms.

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