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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
A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 × 10−7 m2, and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?
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 |
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.
If R1 and R2 are filament resistances of a 200 W and a 100 W bulb respectively, designed to operate on the same voltage, then:
Choose the correct alternative:
The resistivity of the alloy manganin is nearly independent of/increases rapidly with increase of temperature.
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