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प्रश्न
Two wires of equal length, one of copper and the other of manganin have the same resistance. Which wire is thicker?
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उत्तर
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.
संबंधित प्रश्न
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 |
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