Question

A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistances of the combination is ______.

Options

• `R/64`

• `R/32`

• `R/16`

• `R/8`

Answer 1

A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistances of the combination is `bbunderline(R/16)`.

Explanation:

When a resistance R is cut into 8 equal pieces, each piece has a resistance of

R' = `R/8`

Four of each piece are connected in parallel to give

`R_1 = (R')/4 = R/32`

Two such sets are connected now in series to give,

`R_2 = 2R_1`

= `2 xx R/32`

= `R/16`