A wire of resistance `15.0(Omega)`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 .

Explanation

(a) ` R_eff = (((15 xx 5)/6) xx 15/6/((15 xx 5)/6) + 15/6) = (((15 xx 5 xx 15)/(6xx6))/75 +15 /6)`
` = ((15 xx 5 xx 15)/(6 xx 90)) = 25/12 `
` =2.08 Omega `.
(b) Across AC
` R_eff = (((15 xx 4)/6) xx((15 xx 2) /6)/ ((15 xx 4)/6) + ((15 xx2)/6)) =(((15 xx 4 xx 2 xx 15)/(6xx6)/((60+30)/6))`
` = ((15 xx 2 xx 4 xx 15)/ (6 xx 90 ))`
` = 10/3 = 3.33 Omega `
(c) Across A&D
` R_eff = (((15 xx 3)/ 6) xx ((15 xx 3)/6)/((15 xx 3)/6) + ((15 xx 3)/6)) = ((15 xx 3 xx 3 xx 15)/(6 xx 6)/90/6)`
` = ((15 xx 3 xx 3 xx 15 )/(6 xx 90)) = 15/4 = 3.75 Omega ` .