Question

Three resistors each of 4 Ohm are connected in the form of an equilateral triangle. The effective resistance across any two corners is:

• A. Ohm
• B. Ohm
• C. 8 Ohm
• D. 12 Ohm

Answer 1

The correct option is B

Ohm

Let us consider the corners A and B as shown. Let's name the third corner C
To take the equivalent resistance across AB, we need to figure out the possible paths for the current to flow from point A to point B.
The current can take two paths, - one from A to B through C and the other which is directly from A to B.
In the path A - C - B, two resistors, each of 4 Ohm are in series. The effective resistance in this path is 4 + 4 = 8 Ώ.

In the path A - B, the resistance is 4 Ώ
Thus, the circuit reduces to two resistors, 8 Ohm and 4 Ohm, parallel to each other.

So the equivalent resistance= $\frac{4\ast 8}{4+8}=\frac{8}{3}Ohm$.