Question

A uniform wire of resistance $R$ stretched uniformly to n- times and then cut to form five wires of equal length, these wire are arranged as shown in the figure. The effective resistance between the point $\text{A}$ and $\text{B}$ is

• A. $\frac{R}{5n^2}$
• B. $\frac{n^{2}R}{5}$
• C. $\frac{R}{5n}$
• D. $\frac{nR}{5}$

Answer 1

The correct option is B $\frac{n^{2}R}{5}$

The new resistance of the streched wire is,

$R^{{}^{\prime }}=n^{2}R$

The new resistance of each piece is,

$r=\frac{R^{{}^{\prime }}}{5}=\frac{n^{2}R}{5}$

As we can see, the given forms a balanced Wheatstone's bridge.


The effective resistance between the points $\text{A}$ and $\text{B}$ is,


$R_{eq}=\frac{2r}{2}=\frac{n^{2}R}{5}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.