Q. A wire has a resistance of 6$\Omega$. It is cut into two parts and both half values are connected in parallel. The new resistance is

A) 3$\Omega$
B) 6$\Omega$
C) 12$\Omega$
D) 1.5$\Omega$
Explanation

(d) Resistance of original wire is
$R = \rho\frac{l}{A}$
$\rho$ ,being the specific resistance of wire. When the wire is cut in two equal halves then resistance becomes
$R^{'} = \frac{\rho l/2}{A} = \frac{R}{2}$
Thus, the net resistance of parallel combination of two halves is given by
$R_{net} = \frac{R^{'} \times R^{'}}{R^{'} + R^{'}}$
$\ \ \ \ \ \ \ \ \ \ = \frac{R^{'}}{2} = \frac{R}{2 \times 2} = \frac{6}{4} = 1.5\Omega$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.