Question

a uniform conductor of resistance R is cut into 20 equal parts . half of them are connected in series and remaining are connected in parallel . if the combination is connected in series then the effective resistance

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

Answer 1

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

Given,

Resistance $R$ is cut into 20 equal part then each part of resistance will be $R/20$

if Half of them are connected in series then equivalent resistance will be

$10\times \frac{R}{20}=\frac{R}{2}\Omega$

If Half of them are connected in parallel than equivalent resistance will be

$\frac{1}{10}\times \frac{R}{20}=\frac{R}{200}\Omega$

Therefore Total equivalent resistance will be equal to series combination of these two equivalent resistance,

$R_{eq}=\frac{R}{2}+\frac{R}{200}=\frac{100R+R}{200}=\frac{101R}{200}$

Hence, Option (A) is correct option