Five wires each of crosssectional area A and length l are...

Five wires each of crosssectional area $A$ and length $l$ are combined as shown in figure. The thermal conductivity $A$ and $C$ is : $K_{1}$ and $K_{2}$ respectively. The equivalent thermal of copper and steel are resistance between points (a) $\frac{l}{\left(K_{1}+K_{2}\right) A}$ (b) $\frac{2 l}{\left(K_{1}+K_{2}\right) A}$ (c) $\frac{l\left(K_{1}+K_{2}\right)}{K_{1} K_{2} A}$ (d) none of these

Five wires each of crosssectional area $A$ and length $l$ are combined as shown in figure. The thermal conductivity
$A$ and $C$ is :
$K_{1}$ and $K_{2}$ respectively. The equivalent thermal of copper and steel are
resistance between points
(a) $\frac{l}{\left(K_{1}+K_{2}\right) A}$
(b) $\frac{2 l}{\left(K_{1}+K_{2}\right) A}$
(c) $\frac{l\left(K_{1}+K_{2}\right)}{K_{1} K_{2} A}$
(d) none of these

Key Concepts

Thermal Conductivity

Thermal conductivity is a material property that quantifies the rate at which heat is conducted through a material when a temperature gradient is present. It is intrinsic to each material and is used in calculating the heat transfer through objects by relating the heat flow to the material's cross-sectional area and the temperature difference across a given length.

Thermal Resistance

Thermal resistance provides a measure of the opposition a material offers to heat flow. It is analogous to electrical resistance in circuits and is calculated using the relationship R = l/(K A), where l is the length of the material, A is its cross-sectional area, and K is its thermal conductivity. This concept is pivotal in determining how effectively heat is transferred through different materials or composite systems.

Series and Parallel Thermal Resistance Combination

In composite systems where multiple conductive paths exist, thermal resistances are combined similarly to electrical resistances. When heat flows through a series of materials, their thermal resistances add up, whereas, in parallel configurations, the reciprocals of the resistances sum to yield the overall thermal conductance. This concept is essential when analyzing systems with multiple wires or materials working together to transfer heat, as it helps in determining the equivalent thermal resistance between given points.

Transcript

Please give Ace some feedback