Question

A wire of resistance 15.0 Ω is bent to form a regular hexagon ABCDEFA. Find the equivalent resistance of the loop between the points (a) A and B (b) A and C and (c) A and D.

Answer 1

A and B = 2.08 Ω

A and C =  3.33 Ω

A and D = 3.75 Ω

Explanation:

a) A and B

 R(eff) = (15*5/6) * (15/6) / (15*5/6) + (15/6)

 = (15 * 5 * 15 / 6*6) / (75+15 / 6)

 = (15 * 5 * 15) / 6 * 90

 = 25/12

= 2.08 Ω

b) A and C

 R(eff) = (15*4/6) * (15*2/6) / (15*4/6) + (15*2/6)

 = 15 * 4 * 15 * 2 / 6 * 90

 = 10/3

= 3.33 Ω

c) A and D

 R(eff) = (15*3/6) * (15*3/6) / (15*3/6) + (15*3/6)

 = 15 * 3 * 15 * 3 / 6 * 90

 = 15/4

= 3.75 Ω