A strain gauge load cell is a force measuring transducer that uses a strain gauge bridge with four active arms is shown in FIGURE Q3c. It is used to convert a resistance change to a voltage change. R, R2, Rs and Re are resistances and V, is the supply voltage. A, B, C and D are nodes. Prove that the relationship between a change in output voltage, 8V, and a change in resistances, OR1, R2, 8R3 and 8R4 can be approximated by: V,R,R, (R, + R, XR, + R) R, R, ER, SR, SR, SR, R, R. [10 marks) R, KAM v. Output R, R. Vs FIGURE Q3c ii. Propose a design of load cell by a freehand sketch showing the position and orientation of the four active strain gauges, [3 marks)