Question

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of $200$ inches and a diameter of one-quarter of an inch has a resistance of $20$ ohms. Find the electrical resistance in a $500$ inch wire with the same diameter.

• A. $50$ ohm
• B. $60$ ohm
• C. $55$ ohm
• D. None of these

Answer 1

The correct option is A $50$ ohm

$R=K\times L\times \left(\frac{1}{D^2}\right)$
$20=K\times 200\times \left(\frac{1}{{25}^2}\right)$
$20=k\times 200\times 16$
$k=\frac{20}{200\times 16}$
$k=0.00625$
$R=K\times 500\times (\frac{1}{25}{)}^2$
$R=0.00625\times 500\times (\frac{1}{25}{)}^2$
$R=3\times 125\times 16$
$R=50$ ohm