A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is : [figure]
- 16
- 10
- 12
- 14
Answer
(3) 12
Solution
The triangular pyramid (tetrahedron) has 6 equal segments, so each segment has resistance r = R6.
Take A at potential V and B at 0. The other two vertices (top vertex and centre vertex) are placed symmetrically with respect to A and B, so both are at potential V2.
∴ No current flows in the segment joining them; it can be removed.
⇒ Between A and B we have three parallel paths: r (direct), 2r (via top vertex) and 2r (via centre vertex).
1RAB = 1r + 12r + 12r = 2r
⇒ RAB = r2 = R12
∴ n = 12
Answer: (3)