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1 First, we observe that the circuit consists of the parallel combination of three subcircuits: the voltage source, the series combination of R1 and R2 , and the series combination of R3 and Rx Since these three subcircuits are in parallel, the same voltage will appear across each of them, namely, the source voltage, vS Thus, the source voltage divides between each resistor pair, R1 R2 and R3 Rx , according to the voltage divider rule: va is the fraction of the source voltage appearing across R2 , while vb is the voltage appearing across Rx : v a = vS R2 R1 + R 2 and vb = vS Rx R3 + R x

Finally, the voltage difference between points a and b is given by: vab = va vb = vS Rx R2 R1 + R2 R3 + R x

This result is very useful and quite general 2 In order to solve for the unknown resistance, we substitute the numerical values in the preceding equation to obtain 0012 = 12 1,000 Rx 2,000 1,000 + Rx

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(and also, of course, reading and reporting in a nicer format) will make this utility, and others you might write, easier to work with. Generally, you shouldn t try to create sophisticated user interfaces on test projects because, frankly, there isn t time and it s often not necessary; however, with a little effort, you can make your testware more functional and friendly. In Exercise 3-1, Part II, you will add code to make a more useful utility out of this little program. You ll add code that will either create or append to the test results file, depending on whether it s the first time the button is clicked or not. You ll also add code to open and read information from the test results file. Then you ll customize this testware a bit by adding some code and modifying properties so that it s easier to use.

C-11, C-13, and C-14 from Appendix C, you would come up with the following estimates:

circuit of Figure 236 in the electronic les that accompany this book If you have practiced building some simple circuits using Electronics Workbench, you should by now be convinced that this is an invaluable tool in validating numerical solutions to problems, and in exploring more advanced concepts

Strain gauges, which were introduced in a Focus on Measurements section earlier in this chapter, are frequently employed in the measurement of force One of the simplest applications of strain gauges is in the measurement of the force applied to a cantilever beam, as illustrated in Figure 237 Four strain gauges are employed in this case, of which two are bonded to the upper surface of the beam at a distance L from the point where the external force, F , is applied and two are bonded on the lower surface, also at a distance L Under the in uence of the external force, the beam deforms and causes the upper gauges to extend and the lower gauges to compress Thus, the resistance of the upper gauges will increase by an amount R, and that of the lower gauges will decrease by an equal amount, assuming that the gauges are symmetrically placed Let R1 and R4 be the upper gauges and R2 and R3 the lower gauges Thus, under the in uence of the external force, we have: R1 = R4 = R0 + R2 = R3 = R0 R R

where R0 is the zero strain resistance of the gauges It can be shown from elementary statics that the relationship between the strain and a force F

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