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Question: A copper rod (resistivity\( = 2.2 \times {10^{ - 8}}\Omega m\)) and an iron rod (resistivity \( = 1....

A copper rod (resistivity=2.2×10−8Ωm = 2.2 \times {10^{ - 8}}\Omega m) and an iron rod (resistivity =1.1×10−8Ωm = 1.1 \times {10^{ - 8}}\Omega m of same length 70cm each and same diameter 1.4mm1.4mm each are joined in series then the combined resistance is

Explanation

Solution

When the rods are connected in series the identical rate of flow occurs through both parts. But the temperature difference at the different points is going to be varied because of the different heat energy that is received. The total thermal resistance when both the rods are connected in series is equal to the sum of their individual thermal resistances.

Complete answer:
The rate of flow of the heat is inversely proportional to the combination of length area and coefficient of thermal conductivity. Thermal resistance is the amount of opposition to the flow of heat. As the thermal resistance increases, it becomes difficult for the heat energy to flow from one place to another place. Thermal resistance is the same as electric resistance.
Hence by taking the data as given
The resistivity of the copper rodρC=2.2×10−8Ωm{\rho _C} = 2.2 \times {10^{ - 8}}\Omega m, Resistivity of the iron rod ρI=1.1×10−8Ωm{\rho _I} = 1.1 \times {10^{ - 8}}\Omega m Length of both the rods l=0.7ml = 0.7m, Diameter of both the rodsd=0.0014md = 0.0014m, and Cross-sectional area A=πd24A = \dfrac{{\pi {d^2}}}{4}
Thermal resistance can be defined as the ratio of the length of the material to the coefficient of thermal conductivity and the area of cross-section which is given by the relation
RC=ρC×LA{R_C} = \dfrac{{{\rho _C} \times L}}{A} And RI=ρI×LA{R_I} = \dfrac{{{\rho _I} \times L}}{A}which gives us RC=2.2×10−8×0.7(π×0.001424){R_C} = \dfrac{{2.2 \times {{10}^{ - 8}} \times 0.7}}{{(\dfrac{{\pi \times {{0.0014}^2}}}{4})}} and RI=1.1×10−8×0.7(π×0.001424){R_I} = \dfrac{{1.1 \times {{10}^{ - 8}} \times 0.7}}{{(\dfrac{{\pi \times {{0.0014}^2}}}{4})}}
If both the rods are taken in series then we get the combined resistance as Rtotal=RC+RI=4.7×10−2Ω{R_{total}} = {R_C} + {R_I} = 4.7 \times {10^{ - 2}}\Omega (Option A)

Note: When the two materials are connected in series having the same physical dimensions, the rate at which the heat transfer occurs, depends on the temperature gradient and specific thermal characteristics of the material. The thermal resistance can also be termed as the ratio of the temperature difference between the two faces of material and the rate of heat flow per unit area. It is also a function of thickness and thermal conductivity.