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 } $
Click to See Answer :
Thermal Resistance of BC is RBC = RCE = 2R
And , Thermal Resistance of BC is RBD = RDE = R (say)
$latex \displaystyle R = \frac{l}{2KA} $
As , Bridge is balanced , hence no heat current will flow in the rod CD
RBCE = 2R +2R = 4R
RBDE = R+R =2R
Now , RBCE & RBDE are in parallel
$ \displaystyle R’ = \frac{4R\times 2R}{4R+2R} = \frac{4R}{3}$
AS , RAB & R’ are in series
Req = RAB + R’= 4R/3 + R = 7R/3