# Three identical metal rods A, B and C are placed end to end and a temperature difference is maintained between the free ends of A and C. If

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Three identical metal rods A, B and C are placed end to end and a temperature difference is maintained between the free ends of A and C. If the thermal conductivity of B(K_(B)) is twice that of C(K_(C )) and half that of A(K_(A)), (K_(A)=49w//mK) calculate the effective thermal conductivity of the system ?
A. 1/3 K_(A)
B. 3K_(A)
C. 2K_(A)
D. 2/3 K_(A)

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Given, K_(B) = K_(A)//2 and K_(B) = 3K_(C)
K_(C) = K_(A)//6
Rods are in series from so
L/K= I_(1)/K_(A) + I_(2)/K_(B) + I_(3)/K_(C) (therefore l = l_(1)=l_(2)=l_(3)
(3l)/K = l/(K_(A) + l/(K_(A)//2) + l/K_(A)//6
or (3l)/K = 9l/K_(A) or K= (K_(A))/3