Two cylindrical wires of the same material have their lengths in the ratio 2 : 1 and their diameters in the ratio 1 : 3. The ratio of the resistance of thinner wire to that of thicker wire is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 18 : 1
The resistance of a given wire is -
$R=ρ\frac{L}{A}$
where,
$ρ$ = Resistivity (same of both wires)
$L$ = length of wire
$A$ = Cross-sectional Area of the wire
$\frac{R_1}{R_2}=\frac{L_1}{A_1}×\frac{A_2}{L_2}=\frac{2×9}{1.1}=\frac{18}{1}$