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

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

Current Electricity

Solution:

Resistance of each piece $=\frac{R}{20}$
When 10 such pieces are connected in series, its effective resistance is
$R_{S}=\left(\frac{R}{20}\right) \times 10=\frac{R}{2}$
When remaining 10 pieces are connected in parallel, its effective resistance is
$R_{P}=\frac{(R / 20)}{10}=\frac{R}{200}$
When these two combinations are connected in series, its effective resistance is
$R_{\text {eff}}=R_{S}+R_{P}=\frac{R}{2}+\frac{R}{200}=\frac{101}{200} R$