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Two metallic rods, each of length L, area of cross A_(1) and A_(z), having resistivitiesrho_(1) and rho_(2)are connected in parallel across a d.c. battery. Obtain the expression for the effective resistivity of this combination. |
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Answer» Solution :Resistances `R_(1)` and `R_(2)` of two given rods will be: `R_(1)= (rho_(1)L)/(A_(1))` and `R_(2)= (rho_(2)L)/(A_(2))` `:. ` EFFECTIVE resistance of PARALLEL combination `R = (R_(1)R_(2))/(R_(1)+R_(2))=((rho_(1)L)/(A_(1))xx (rho_(2)L)/(A_(2)))/(((rho_(1)L)/(A_(1))+rho_(2)L))impliesR=(rho_(1)rho_(2)L)/((rho_(1)A_(1)+rho_(2)A_(2)))` Moreover, since length of both rods is same, effective EQUIVALENT AREA A `= (A_(1)+A_(2))` `:.` Effective resistivity `rho- (RA)/(L) - (rho_(1)rho_(2)(A_(1)+A_(2)))/((rho_(1)A_(2)+rho_(2)A_(1)))` |
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