To determine the resistance between A and B, we can consider the equivalent resistance between A and B in the triangular lattice with the wire connecting B and C cut off.
Without loss of generality, let's assign a resistance of R/2 to the wire connecting B and C. This is because cutting off the wire effectively results in two parallel resistors, each with a resistance of R/2.
Now, let's consider the triangular lattice with the wire connecting B and C cut off. We can see that there are two paths from A to B:
1. Path 1: A --> B directly
2. Path 2: A --> C --> B
Path 1 has a total resistance of R/2, as there is only one resistor along this path.
Path 2 has a total resistance of 2(R/2) = R, as there are two resistors in parallel along this path.
Since the two paths are in parallel, the equivalent resistance between A and B is given by the formula:
1/Req = 1/(R/2) + 1/R
Simplifying this expression gives:
1/Req = 2/R + 1/R
1/Req = 3/R
Therefore, the equivalent resistance between A and B is R/3.
Answer: (a.) R/3
There is an infinite triangular lattice; the edges of the lattice are made of wire, and the resistance of each edge is R. Let us denote the corners of a triangular lattice face by A, B, and C. The wire connecting B and
C
is cut off. Determine the resistance between A and B. (a.)
1 answer