A strain gage in a Wheatstone bridge to form a quarterbeam c

A strain gage in a Wheatstone bridge to form a quarter-beam circuit (with all resistors at first equal to R = 1, 900 Ohm and the source voltage is Vs - 5 V) is subjected to strain. The system output is Vo = 4.0 mV. What is the change in resistance (delta R) of the strain gage in Ohm?

Solution

The resistance of the gauge is given the Voltage relation,

Vo = ( R3 / R3+R4) Vs - (R1 / R1 + R2) Vs

Rearranging for R4 gives the relation,

R4 = [(Vo + (R1/R1+R2)Vs)*1/R3*Vs]^-1 - 1.9

The value of R4 corresponding to the strain in the system is 1.90343 ohm

The change in resistance is del R = 1.90343 - 1.9 = 0.0343 or 3.43 x 10^-2 ohm