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

Options

A. R
B. `(R)/(2)`
C. `(101 R)/(200)`
D. `(201 R)/(200)`

Answer

C

Explanation

`(101 R)/(200)`
Resistance of each part when wire is div.ided into 20 equal parts = `(R)/(20)`
Equivalent resistance of 10 such parts joined in series is,
`R_(1) = (10 R)/(20) = (R)/(2)`
Equivalent resistance of 10 remaining parts when joined in parallel,
`R_(2) = (R)/(200)`
Equivalent resistance of circuit,
R = `R_(1) + R_(2)`
`= (R)/(2) + (R)/(200) = (100 R + R)/(200) = (101)/(200) ` R