Question

A uniform conductor of resistance R is cut into $10$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If these two combination are joined in series, then the effective resistance of the pieces is?

• A. $\frac{13}{25}$R
• B. $\frac{R}{2}$
• C. $\frac{R}{15}$
• D. $\frac{25}{11}$R

Answer 1

Answer: (A)

$\frac{13}{25}$R

A uniform rod of resistance R, when cut into $10$ equal pieces, then the resistance of each piece is $\frac{R}{10}$. $5$ such resistances $\left(\frac{R}{10}\right)$ are connected in series.
So, $R_s=5\times \frac{R}{10}=\frac{R}{2}$
Also remaining $5$ resistances $\left(\frac{R}{10}\right)$ are connected in parallel.
So, $R_P=\frac{\frac{R}{10}}{5}=\frac{R}{50}$
When, $R_S$ and $R_P$ are connected in series, then
$R_{eff}=R_S+R_P=\frac{R}{2}+\frac{R}{50}$
$=\left(\frac{25+1}{50}\right)R$
$\therefore R_{eff}=\frac{13}{25}R$.