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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 . |
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Answer» Solution :(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 ` . |
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