Question

Three metal rods of same length and same cross sectional area are connected in parallel. If there conductivities are 70WmK, 110WmK and 180WmK respectively then effective conductivity of the combination is

Answer 1

Answer:

As conductivity is inversely proportional to resistance we will add up all to get equivalent conductivity.

Answer 2

Answer:

Effective conductivity of the combination of three metal rods is $360Wm^{-1}K^{-1}$.

Explanation:

Thermal conductivity is a property related to the property of material.

If The length of a rod is L and the surface area of material (cross-section of the rod) is A . Let T1 is the temperature of the first end of the rod and the T2 is the temperature of the other end of the rod. Then the temperature difference will become (T2−T1) . If Q is the quantity of heat flow then the thermal conductivity of the rod k is given as-

$k=\frac{QL}{A(T_{2}-T_{1} )}$

So, the coefficient of thermal conductivity of rod depends on the following as per the formula-

• -Change in temperature
• Length of the rod.
• Material of the rod.
• Cross-section of the rod

Given: Thermal conductivity of first rod,$k_{1} =70Wm^{-1} K^{-1}$

Thermal conductivity of second rod, $k_{2} =110Wm^{-1} K^{-1}$

Thermal conductivity of third rod, $k_{3} =180Wm^{-1} K^{-1}$

Total conductivity,$k=k_{1} +k_{2}+k_{3}$

$k=(70+110+180)Wm^{-1} K^{-1} \\k=360Wm^{-1} K^{-1}$

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