resistors cube
Submitted by: I.D. 066101528
The problem:
In the resistors cube you see in the sketch all resistors are equal and their resistance is R.
1. Find the equivalent resistance between points a and b.
2. How does the equivalent resistance changes if we connect point 4 with point 5 with a resistor
R?
The solution:
1. We can easily see that the cube is symmetrical for a current to junction 4 and 5 therefore the
potential is equal in those two points, same about points 3 and 6. If the potential is equal it means
that we can connect these two junctions into one and create the electrical circuit you see in sketch
1.
We simplify circuit 1 by connecting all the resistors in parallel into one resistor:
1
1
R
1
= + ⇒ Rt =
Rt
R R
2
now we have a circuit like in sketch 2.
1
We simplify circuit 2 by connecting all the resistors in row into one resistor:
Rt =
R
R
+ R + = 2R
2
2
now we have a circuit like in sketch 3.
We simplify circuit 3 by connecting all the resistors in parallel into one resistor:
1
2
1
2R
= +
⇒ Rt =
Rt
R 2R
5
now we have a circuit like in sketch 4.
We simplify circuit 4 by connecting all the resistors in row into one resistor:
Rt =
R 2R R
7R
+
+ =
2
5
2
5
now we have a circuit like in sketch 5.
We simplify circuit 5 by connecting all resistors in parallel into one resistor:
1
1
5
7R
= +
⇒ Rt =
Rt
R 7R
12
we found the equivalent resistance between points a and b to be
Rt =
7R
12
2. Of course, the equivalent resistance would not change - that is because the potential between
those two points is zero, therefore, there would be no current and the resistance would not change!
2