A group of students wants to determine the internal resistance of a battery. They connect the battery to a variable resistor. The students measure the potential difference across the battery as a function of the current through the battery as they vary the resistance. Which of the following analyses of the data could be used to determine the internal resistance of the battery?

a. Divide the potential difference across the battery by the current through it for each data point. The average of these calculations gives the internal resistance of the battery.

b. Graph the potential difference across the battery as a function of the current through it. Extrapolate to find the y- intercept and divide this by the average of the current measurements to find the internal resistance of the battery.

c. Find the best-fit straight line for a graph of potential difference across the battery as a function of the current through it. The absolute value of the slope represents the internal resistance of the battery.

d. This data cannot be analyzed to give the internal resistance of the battery, because the potential difference across the battery does not depend on the current.

Atension test was conducted on a specimen of aisi 1020 hot-rolled steel having an initialdiameter of 9.11 mm. representative test data are given in table1in the form of force and engineering strain. for strain the extensometer gage length was li= 50.8 mm. in addition, minimumdiameters were measuredmanually with a micrometer in the necked region at several points during the test. after fracture, thebroken halves were reassembled, and the following measurements were made: (1) marks originally 25.4 mm apart and on opposite sides of the necked regionwere 38.6 mm apart due to the lengthwise stretching in the specimen; (2) similar marks originally 50.8 mm apart were 70.9 mmapart; (3) the final minimum diameter in the necked region was 5.28 mma) determine the following material properties: elastic modulus, 0.2% offset yield strength, ultimate tensile strength, percent elongation, and percent reduction in area. b) assume that the test was interrupted upon reaching a strain u = 0.007, and the specimen unloaded to zero force. estimate the elastic strain recovered and the plastic strain remaining. also, what would the new length of the original 50.8 mm gage section. hint: might save time/effort to use excel, mathcad, matlab, etc. to solve part a)table1 data and analysis for a tension test on aisi 1020 hot-rolled steeltest dataforce (p, kn)1. 0.002. 6.673. 13.344. 19.135. 17.796. 17.217. 17.538. 17.449. 17.2110. 20.7711. 24.2512. 25.7113. 25.7514. 25.0415. 23.4916. 21.3517. 18.9018. 17.39engr. strain (ε)1. 02. 0.00053. 0.00104. 0.00155. 0.00236. 0.00317. 0.00508. 0.00709. 0.010010. 0.049011. 0.125012. 0.218013. 0.234014. 0.306015. 0.330016. 0.348017. 0.360018. 03660diameter (d, mm)1. 9.112. 9.113. 9.114. 9.115. 9.116. 9.117. 9.118. 9.119. 9.1110. 8.8911. 8.8912. 8.2613. 8.2614. 7.6215. 6.9916. 6.3517. 5.7218. 5.28