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)

$\frac{R}{16}$

Answer 2

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 $\frac{1}{R'}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\frac{1}{R_{4}}$ $\therefore \frac{1}{R'}=\frac{4}{R''}=\frac{4 \times 4}{R}$ $\Rightarrow R'=\frac{R}{16}$