This question involves the concepts of the resistance, resistivity, and length.
The ratio of the resistivity of the two resistors is "0.5".
RESISTIVITY
Resistance of a wire can be given in terms of resistivity through following formula:
[tex]R=\frac{\rho L}{A}[/tex]
where,
- R = resistance
- [tex]\rho[/tex] = resistivity
- L = length
- A = area of cross-section
Using subscript 1 for first resistor:
[tex]R_1=\frac{\rho_1 L_1}{A_1}[/tex]
Using subscript 2 for first resistor:
[tex]R_2=\frac{\rho_2 L_2}{A_2}[/tex]
Dividing both equations:
[tex]\frac{R_1}{R_2}=\frac{\frac{\rho_1 L_1}{A_1}}{\frac{\rho_2 L_2}{A_2}}[/tex]
It is given that:
Therefore,
[tex]1=\frac{\rho_1(2L_2)}{\rho_2(L_2)}[/tex]
[tex]\frac{rho_1}{\rho_2}=0.5[/tex]
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