Question

The resistance of certain piece of wire is 9 $\Omega$, the resistance of second piece, identical to first, except that its diameter is 3 times as large will be (in $\Omega$) :

• A. 1
• B. 3
• C. 9
• D. 27

Answer 1

The correct option is A 1

$R=\rho \frac{L}{A}$

$⟹R=\rho \frac{4L}{D^2}$ where $D=$ diameter

$⟹R\propto \frac{1}{D^2}$

Hence, on increasing diameter to $3$ times, its resistance becomes $\frac{1}{9}$ times.

Hence, $R=\frac{1}{9}\times 9\Omega$

$⟹R=1\Omega$

Answer-(A)