Question

Test 4 tem de Time 00:36:46 8 of 23 Awre of length and cross sectional wrea A has resistance R Constants Part A What will be the resistance Read of the wet is stretched to twice s original length? Assume that the density and resistivity of the material do not change when the wris stretched Express your answer in terms of the wire's original resistance R. 0 AED Re Subme Best AS Provide Feedback Next >

Answer 1

Objective : to find the resistance Ristoetbed of the wire. Answer : Given in formation, Initiully, Length of the wire = b C305S- Sectional 0704 = A Resistance of wire R The wire is stretched to twice of the original length. Final length of the wire will be al. Let us assume that the initial diameter of wire is 'd'. It is mentioned that the density of wire is constant, that means, total volume of the wire remains same after stretch. Initial volume of the wire, Vi = Area of cross-section x Length :: Vi=d).(2) Final volume of the wire, Uf = Final crrey of moss-sections final length .: Vf (I do?). (26) where df = final diameter of wide. As we know that, Initial volume = Vi Vf (2L) ). df Final Volume '. L - ds. 2 2 d 0.50? Initial Resistance of wire is given by, L R = А where, 9 = zesistivity of wire , which is constemt.

:: R - S L ... (1) I d² Final Resistance of wire. Rstretched (22) S: Af .. R ste tched (2L) s ..(ii) Take jutio of equation (i) and (i), (24) Ristetched S: R S srd (Ads) R Stretched R 202 dg² but df = 0.5d² :. R stretched R 2d2 0.5d² Rstretched 2 4 R 0.5 Rstretched 4R The resistance Rstretched of the wire in terms of original resitance R Rstretched 4R