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Question
Two wires of equal length, one of copper and the other of manganin have the same resistance. Which wire is thicker?
Solution
Since the resistivity of alloy is greater than the resistivity of its constituents. We have resistivity of manganin greater than resistivity of copper metal.
So, Resistance `R = ρ1/A`
Where l is length and A is area of cross-section of material.
Also ρ is the resistivity of the material.
For copper, `R_c = ρ_c l_c/A_c`
and for magnanin `R_m = ρ_m l_m/A_m`
We have
`ρ_m>ρ_c`
`or ρ_m/ρ_c > 1`
`As l_c = l_m`
Dividing `R_c/R_m = (ρ_cA_m)/(ρ_mA_c)`
Again `R_c = R_m`
`therefore ρ_c A_m = ρ_mA_c`
`ρ_m/ρ_c=A_m/A_c >1`
Hence `A_m >A_c`
Or, Manganin wire is thicker.
RELATED QUESTIONS
Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables.
(ρAl = 2.63 × 10−8 Ω m, ρCu = 1.72 × 10−8 Ω m, Relative density of Al = 2.7, of Cu = 8.9.)
What conclusion can you draw from the following observations on a resistor made of alloy manganin?
| Current A |
Voltage V |
Current A |
Voltage V |
| 0.2 | 3.94 | 3.0 | 59.2 |
| 0.4 | 7.87 | 4.0 | 78.8 |
| 0.6 | 11.8 | 5.0 | 98.6 |
| 0.8 | 15.7 | 6.0 | 118.5 |
| 1.0 | 19.7 | 7.0 | 138.2 |
| 2.0 | 39.4 | 8.0 | 158.0 |
Choose the correct alternative:
Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
Two resistors A and B have resistances RA and RB, respectively, and RA < RB. The resistivities of their materials are ρA and ρB.
How does the resistivity of a semiconductor change with rise of temperature ? Explain.
Choose the correct alternative:
The resistivity of the alloy manganin is nearly independent of/increases rapidly with increase of temperature.
Choose the correct alternative:
The resistivity of a typical insulator (e.g., amber) is greater than that of a metal by a factor of the order of (1022/1023).
