Question

A wire is cut into four pieces, which are put together by sides to obtain one conductor. If the original resistance of wire was $ R $ , the resistance of the bundle will be:

• A. $ \frac{R}{4} $
• B. $ \frac{R}{8} $
• C. $ \frac{R}{16} $
• D. $ \frac{R}{32} $

Answer 1

Answer: (C)

For a wire of length $l$, area of cross-section $A$, and specific resistance $\rho$, the resistance is given by
$R=\frac{\rho l}{A}$
From above equation it is clear that resistance is directly proportional to length. When wire is cut into 4 pieces then resistance of each part is
$R'' \propto \frac{l}{4} $
$\Rightarrow R'' =\frac{R}{4}$
Also, equivalent resistance for parallel combination is
$\frac{1}{R'}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\frac{1}{R_{4}}$
$\therefore \frac{1}{R'}=\frac{4}{R''}=\frac{4 \times 4}{R}$
$\Rightarrow R'=\frac{R}{16}$