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Question

A uniform conductor of resistance R is cut into $$20$$ equal pieces half of them are joined is series and the remaining half of them are connected in parallel if the two combination are joined in series


Solution

let the resistance of each piece $${ R }_{ 0 }$$
where$${ R }_{ 0 }$$ $$R/20$$
so we have 10 such resistance joined in resistance thus giving us an $${ R }_{ eq\quad series }=10\times { R }_{ 0 }=10{ R }_{ 0 }$$
the 10 resistance joined in parallel which gives us an equilance 
$${ R }_{ eq\quad parallel }=10/{ R }_{ 0 }\quad this\quad combination\quad joined\quad in\quad series\quad { R }_{ net\quad  }={ R }_{ 0 }/10=10{ R }_{ 0 }$$
$${ R }_{ net\quad  }=101{ R }_{ 0 }/10=101\times R/200$$

Physics

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