1.

A and B are two points on a uniform metal ring whose centre is C. The angle ACB = θ. A and B are maintained at two different constant temperatures. When θ = 180°, the rate of total heat flow from A to B is 1.2 W. When θ = 90°, this rate will be (a) 0.6 W (b) 0.9 W (c) 1.6 W (d) 1.8 W

Answer»

Correct Answer is: (c) 1.6 W 

Let R = total thermal resistance of the ring,

ΔT = difference in temperature between A and B.

For θ = 180°, two sections of resistance R/2 each are in parallel.

Equivalent resistance = R/4.

Rate of total heat flow = I1 = 1.2 = ΔT/R/4

or 0.3 = ΔT/R

For θ = 90°, two sections of resistances R/4 and 3R/4 are in parallel.

Equivalent resistance = (R/4)(3R/4) / R/4 

= 3R/4 

= 3R/16 . 

Rate of total heat flow

I2 = ΔT/3R/16 W 

= 16/3 (ΔT/R) W 

= 16/3 x 0.3 W 

= 1.6 W.



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