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the resistance of a solution "A" IS 50 OHMS AND THAT OF SOLUTION 'B' IS 100 OHMS BOTH SOLUTIONS BEING TAKEN IN THE SAME CONDUCTIVE CELL
IF EQUAL VOLUMES OF SOLUTION  A   AND  B  ARE MIXED WHAT WILL BE THE THE RESISTANCE OF THE MIXTURE USING THE SAME CELL. 

Asked by sudheerkapoor67 9th October 2017, 6:08 PM
Answered by Expert
Answer:
Assume that K1 and K2 be the conductivity of the solution A and B respectively and the constant of the cell be 'x'.
Thus, for solution A, conductivity = Conductance x cell constant
begin mathsize 18px style K subscript 1 space equals space 1 over 50 cross times space x space space.... space left parenthesis 1 right parenthesis

F o r space s o l u t i o n space B comma space c o n d u c t i v i t y space K subscript 2 space equals space 1 over 100 cross times space x space space space space.... left parenthesis 2 right parenthesis
S i n c e space e q u a l space v o l u m e s space o f space A space a n d space B space a r e space m i x e d comma space b o t h space t h e space s o l u t i o n s space g e t space d o u b l y space d i l u t e d comma space
h e n c e space t h e i r space i n d i v i d u a l space c o n t r i b u t i o n space t o w a r d s space t h e space c o n d u c t i v i t y space o f space t h e space m i x t u r e space w i l l space b e space left parenthesis K subscript 1 divided by 2 right parenthesis space a n d space left parenthesis K subscript 2 divided by 2 right parenthesis space r e s p e c t i v e l y space
a n d space t h e space c o n d u c t i v i t y space o f space t h e space m i x t u r e space w i l l space b e space left parenthesis 1 divided by 2 right parenthesis left parenthesis K subscript 1 plus K subscript 2 right parenthesis
H e n c e comma space f o r space t h e space m i x t u r e comma space space 1 divided by 2 left parenthesis K subscript 1 plus K subscript 2 right parenthesis space equals space left parenthesis 1 divided by R right parenthesis cross times space x space space....... left parenthesis 3 right parenthesis
left parenthesis R space i s space t h e space r e s i s t e n c e space o f space t h e space m i x t u r e right parenthesis
F r o m comma space e q u a t i o n s space 1 comma space 2 comma space a n d space 3 comma
R space equals space 66.67 space o h m
end style
Answered by Expert 10th October 2017, 12:35 PM
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