The rod given in the figure is made up of two different materials. Both have square cross sections of 3 mm side. The resistivity of the first material is 4 xx 10^(-3) Omega.m and it is 25 cm long while second material has resistivity of 5 xx 10^(-3) Omega.m and is of 70 cm long. What is the resistivity of rod between its ends?

iarc6io 2022-07-16 Answered
The rod given in the figure is made up of two different materials. Both have square cross sections of 3 mm side. The resistivity of the first material is 4 × 10 3 Ω . m and it is 25 cm long while second material has resistivity of 5 × 10 3 Ω . m and is of 70 cm long. What is the resistivity of rod between its ends?
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Answers (1)

Arthur Gillespie
Answered 2022-07-17 Author has 10 answers
Side of square cross section , a = 3   m m = 3 × 10 3   m
Cross section , A = a 2 = ( 3 × 10 3 ) 2 = 9 × 10 6   m 2
Resistivity of first material , ρ 1 = 4 × 10 3 Ω . m
Resistivity of second material , ρ 2 = 5 × 10 3 Ω . m
length of first material , L 1 = 25   c m = 0.25   m
length of second material , L 2 = 70   c m = 0.7   m
To find = Resistivity of rod
We can calculate the resistance due to the first material using :
R 1 = ρ 1 L 1 A R 1 = 4 × 10 3 × 0.25 9 × 10 6 R 1 = 111.11   Ω
Similarly , we can calculate the resistance due to second material using :
R 2 = ρ 2 L 2 A R 2 = 5 × 10 3 × 0.7 9 × 10 6 R 2 = 388.89   Ω
Since they are connected in series , the total resistance is :
R = R 1 + R 2 R = 111.11 + 388.89 R = 500   Ω
Hence, the total resistance of the rod is 500   Ω
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