CBSE Class 12-science Answered
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Asked by jain.pradeep | 29 Feb, 2020, 10:46: AM
Expert Answer
If current flowing through two sets is same, then their resistances are equal.
Resistance of set-1 wire, R1 = ρ1 l / A1
Resistance of set-2 wire, R2 = ρ2 l / A2
Where ρ is respective resistivity of material of wire of each set,
l is the equal length of wire and A is respective area of cross section.
Since R1 = R2 , we have, ρ1 l / A1 = ρ2 l / A2
Hence, we get , ( ρ1 / ρ2 ) = ( A1 / A2 ) ........................ (1)
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if the balancing length lb is less than l/2, obviously for both set, balancing length is equal.
If balancing length is greater than l/2, let us assmy , lb = ( l/2 ) + x
the excess resistance Rx in set-1 = ρ1 x / A1 ...................(2)
using eqn.(1), we have, ( ρ1 / A1 ) = ( ρ2 / A2 )
hence eqn.(2) bexomes, Rx = ρ2 x / A2 , which is same as excess resistance in set-2.
Hence balancing legths will be equal for both the set
Answered by Thiyagarajan K | 01 Mar, 2020, 08:56: AM
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