A wire of resistance $R$ is cut into 6 equal pieces. From these pieces, two separate equivalent resi

Question

A wire of resistance $R$ is cut into 6 equal pieces. From these pieces, two separate equivalent resistances are made by adding three pieces together in parallel for each set. These two sets are then connected in series. The net effective resistance of the final combination is

Professor PC Thomas Classes · Answer

(b) : The resistance of each individual piece is $r = R/6$. A set of 3 such pieces connected in parallel has an equivalent resistance of $R_1 = \frac{r}{3} = \frac{R/6}{3} = \frac{R}{18}$. Since there are two such identical sets, $R_2$ is also $R/18$. When these two sets are connected in series, the net effective resistance is $R_{eq} = R_1 + R_2 = \frac{R}{18} + \frac{R}{18} = \frac{2R}{18} = \frac{R}{9}$.