If five equal pieces of a resistance wire having `5 Omega` resistance are connected in parallel, their equivalent resistance will be …………… .

Options

A. `1/5 Omega`
B. `1 Omega`
C. `5Omega`
D. `25 Omega`

Answer

A

Explanation

When a resistance wire having `5 Omega` resistance is cut into five equal pieces, each piece will have resistance `1 Omega`, i.e., `R_1 = R_2 = R_3 = R_4 =R_5 =1 Omega`.
The equivalent resistance (`R_p`) of their parallel combination is given by,
`1/R_p = 1/R_1 + 1/R_2 + 1/R_3 + 1/R_4 + 1/R_5`
`:. 1/R_p = 1/1+ 1/1 + 1/1 + 1/1 + 1/1`
`:. 1/R_p = 5/1`
`:. R_p = 1/5 Omega`