Question

A uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series, the effective resistance of the combination is-

• A. $\frac{R}{2}$
• B. $\frac{201R}{200}$
• C. $R$
• D. $\frac{101R}{200}$

Answer 1

The correct option is D $\frac{101R}{200}$

Given, a uniform wire of resistance $R$ cut into $20$ equal pieces.

Resistance of a wire is,

$R=\frac{\rho l}{A}\Rightarrow R\propto l$

Resistance of each piece of wire will be, $R^{{}^{\prime }}=\frac{R}{20}$

Now, $10$ pieces are connected in series and the remaining are connected in parallel.

Let, effective resistance in series and parallel be $R_s$and $R_p$

$R_s=10R^{{}^{\prime }}=\frac{R}{2}$

$R_p=\frac{R^{{}^{\prime }}}{n}=\frac{R^{{}^{\prime }}}{10}=\frac{R}{200}$

Finally, $R_s$ and $R_p$ are connected in series,

$R_{eff}=R_s+R_p$

$=\frac{R}{2}+\frac{R}{200}=\frac{101R}{200}$

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