Question

A battery of 10V and negligible internal resistance is connected across the diagonally opposite corners of a cubical network consisting of 12 resistors each of 1$\Omega$ resistance. Use Kirchhoff’s rules to determine:
(a) the equivalent resistance of the network.
(b) the total current in the network.

Answer 1

Welcome dear,

● Answer -
R' = 5/6 ohm
I = 4 A

● Explaination -
[Refer to the image attachment for diagram.]

Let V be EMF of cell. Due to symmetry of the cube, we can say that same current I flows through all the resistors.

Using Kirchoff's 2nd law,
-IR - (1/2)IR - IR + V = 0
V = 5/2 IR
I = 2V / 5R

Effective resistance of network is calculated by -
R' = V / 3I
R' = 5/6 R
R' = 5/6 ohm

Current flowing through each edge is -
I = 2V / 5R
I = 2×10 / 5×1
I = 4 A

Hope this helps you...

Answer 2

Thanks for question

I hope it's help you......