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Question

# Find the ratio of resistances of two copper rods X and Y of lengths 30 cm and 50 cm respectively and having a radii 3 cm and 2 cm respectively. ​​​​​​​

A
5:3
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B
3:5
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C
4:15
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D
15:4
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Solution

## The correct option is C 4:15Resistance (R) of a conductor depends on (i) it's length (L) (ii) it's area of cross-section (A) and (iii) the resistivity of the material (ρ) R=ρ LA RX=ρX LXAX=ρX 30π×3×3 RY=ρY LYAY=ρY 50π×2×2 Since both the rods are made of copper only, therefore, ρX=ρY ⟹RXRY=30×π×2×250×π×3×3 ⟹RXRY=415 Hence the ratio of resistances of wires X and Y will be 4:15.

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