Question

12 wires of equal length and same cross section are connected in the form of a cube is the resistance of each of the wire is r then the effective resistance between the two diagonal ends would be

Answer 1

Simplified circuit diagram for the given question is attached in my answer.

Lets find equalatent resistance for Part A.

Clearly, 3 resistors of resistance r are in parallel.

So Equalent resistance = r/3 (1)

For Part B,
6 resistors of resistance r are in parallel.

So equalent resistance = r/6 (2)

For part C,
3 resistors of resistance r are in parallel.

So equalent resistance = r/3. (3)

As part A, part B and part C are in series so

Equalent resistance for whole circuit will be

(1)+(2)+(3)

r/3 + r/6 +r/3

So answer comes out to be

$\huge \bold { \frac{5r}{6}}$

Answer 2

Answer:

5r/6

Explanation:

Simplified circuit diagram for the given question is attached in my answer.

Lets find equalatent resistance for Part A.

Clearly, 3 resistors of resistance r are in parallel.

So Equalent resistance = r/3 (1)

For Part B,

6 resistors of resistance r are in parallel.

So equalent resistance = r/6 (2)

For part C,

3 resistors of resistance r are in parallel.

So equalent resistance = r/3. (3)

As part A, part B and part C are in series so

Equalent resistance for whole circuit will be

(1)+(2)+(3)

r/3 + r/6 +r/3

So answer comes out to be

5r

6