Question

A wire of 9 ohm resistance having 30 cm length is tripled on itself. What is its new resistance?

• A. $81\Omega$
• B. $9\Omega$
• C. $3\Omega$
• D. $18\Omega$

Answer 1

The correct option is A $81\Omega$

When we stretch a wire to make its length double or whatever the size, to conserve volume, its cross sectional area must decrease. For a common observation, when we stretch something its length increases but thickness decreases. Now the tricky part is in the question we are being told the new length but not the cross sectional area so we have to find it first.

Let's say a wire having length L cross sectional area A have resistance R. If it is so stretched that its length becomes 3L so new length L' = 3L and when length is tripled by stretching the cross sectional area decreases to one-third.

The resistance of the wire is expressed as $R=\frac{\rho L}{A}$where,

rho is the resistivity of the wire,

L is the length of the wire,

A is the area of coss section of the wire.

The new resistance is calculated as follows.

$R=\frac{\rho 3L}{\frac{A}{3}}=\frac{9\rho L}{A}$.

That is, the new resistance is nine times the old resistance.

Hence, the new resistance is $9\times 9=81ohms$.