Two conductors are made of the same material and have the same le… - Vidyadip

MCQ

Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1.0\, mm$. Conductor $B$ is a hollow tube of outside diameter $2.0\, mm$ and inside diameter $1.0\, mm$. The resistance ratio $R_A/R_B$ will be

A
$1$
B
$2$
✓
$3$
D
$4$

✓

Answer

Correct option: C.

$3$

c
For conductor $A$, ${R_A} = \frac{{\rho \,l}}{{\pi r_1^2}}$,

For conductor $B$, ${R_B} = \frac{{\rho \,l}}{{\pi (r_2^2 - r_1^2)}}$

$ \Rightarrow $ $\frac{{{R_A}}}{{{R_B}}} = \frac{{r_2^2 - r_1^2}}{{r_1^2}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2} - 1 = {\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^2} - 1 = {\left( {\frac{2}{1}} \right)^2} - 1 = 3$

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