Question

The resistance of a 10 cm long wire is 12 Ω. If this wire is doubled on itself and included in a circuit, what will be the resistance of this wire?

• A. $3\Omega$
• B. $4\Omega$
• C. $5\Omega$
• D. $6\Omega$

Answer 1

The correct option is A

$3\Omega$

Let the length of the conductor be $l$ and cross-sectional area be $A.$

Resistance(R) of the wire will be $R=\rho \frac{l}{A}$ where $\rho$ is its resistivity.

Given: $R=12\Omega$
New length, $l^{\prime }=\frac{l}{2}$
New cross-sectional area, $A^{\prime }=2A$

Therefore, the new resistance $R^{\prime }=\rho \frac{l^{\prime }}{A^{\prime }}=\rho \frac{l}{2\times 2A}=\frac{1}{4}\rho \frac{l}{A}=\frac{1}{4}\times 12=3\Omega$