# Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle ABC right angled at B….

Q: Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle ABC right angled at B. The points A and B are maintained at temperatures T and √2 T , respectively, in the steady state. Assuming that only heat conduction takes palace, temperature of point C is

(a) $\displaystyle \frac{3T}{\sqrt{T} + 1 }$

(b) $\displaystyle \frac{T}{\sqrt{T} + 1 }$

(c) $\displaystyle \frac{T}{3(\sqrt{T} + 1 )}$

(d) $\displaystyle \frac{T}{\sqrt{T} – 1 }$

Ans: (a)
Sol:

RAB = RBC = R

RAC = √2 R

Since TB > TA , heat will flow from B to A through two paths BA and BCA.

In path BCA, current will be same in BC and CA

Let temp. of point C = TC

$\displaystyle I = \frac{\sqrt 2 T – T_C}{R_{BC}} = \frac{T_C – T}{R_{AC}}$

$\displaystyle \frac{\sqrt 2 T – T_C}{R} = \frac{T_C – T}{\sqrt 2 R}$

2T -√2 TC = TC – T

(√2 + 1)TC = 3T

$\displaystyle T_C = \frac{3T}{\sqrt 2 + 1}$