Q: Three rods of material ‘x’ and three rods of material y are connected as shown in figure. All the rods are of identical length and cross-section. If the end A is maintained at 60°C and the junction E at 10°C, find effective Thermal Resistance. Between A and E, Given length of each rod = *l*, area of cross-section = A, conductivity of x = K and conductivity of y = 2K.

(a) $ \displaystyle \frac{4l}{3 K A} $

(b) $ \displaystyle \frac{7l}{6 K A} $

(c) $ \displaystyle \frac{4 K A}{3 l} $

(d) $ \displaystyle \frac{7 K A}{3 l } $

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Thermal Resistance of BC is R_{BC} = R_{CE} = 2R

And , Thermal Resistance of BC is R_{BD} = R_{DE} = R (say)

$latex \displaystyle R = \frac{l}{2KA} $

As , Bridge is balanced , hence no heat current will flow in the rod C*D*

R_{BCE = }2R +2R = 4R

R_{BDE} = R+R =2R

Now , R_{BCE} & R_{BDE} are in parallel

$ \displaystyle R’ = \frac{4R\times 2R}{4R+2R} = \frac{4R}{3}$

AS , R_{AB} & R’ are in series

R_{eq} = R_{AB} + R’= 4R/3 + R = 7R/3