Question 585: Current Electricity

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 resistance of the combination is:

Accepted Answer

After cutting the wire into 8 equal pieces:
Resistance of each piece:
Each piece has a resistance $R' = \frac{R}{8}$.
Parallel Combination in Each Set:
Each set consists of 4 pieces connected in parallel:
Resistance of each set:
$      R'' = \frac{R'}{4} = \frac{R}{32}      $
Connecting the Sets in Series:
With both sets connected in series, the equivalent resistance is calculated as:
$    R_{	ext{eq}} = R'' + R'' = 2 	imes \frac{R}{32} = \frac{R}{16}    $
Thus, the net effective resistance of the combination is $\frac{R}{16}$.

Answer

$\frac{R}{16}$

Answer

$\frac{R}{8}$

Answer

$\frac{R}{64}$

Answer

$\frac{R}{32}$

Current Electricity

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 resistance of the combination is:

Choose the correct answer: