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  4. A uniform conductor of resistance R is cut into 20 equal pieces. Half of them is 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 all the pieces will be

Q. A uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them is 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 all the pieces will be

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Solution:

If resistance $R\, \Omega$ is cut into $20$ pieces, then resistance of each part becomes $R / 20$.
If half of the pieces i.e.$10$ pieces are joined in series.
$R_{ s }=10(R / 20)$ $=R / 2$.
other $10$ pieces are joined in parallel.
Since $R_{ P }= R / n =( R / 20) / 10= R / 200$
If $R / 2$ and $R / 200$ are connected in series again, the effective resistance is
$R_{ S }=(R / 2)+(R / 200)$
$=100\, R + R / 200=101\, R / 200$.

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