Question

fig shown on the right hand side represent a 5 pointed regular star made fron a uniform wire .calculate

a.the resistance of the section BN

b.resistance of the triangle and

c. total resistance across M and N.

Answer 1

Answer:

0.62r

Explanation:

since the given star is regular

therefore triangles ABN, NHG, GFE, EMD, DCB all are Congruent to each other.

hence, BNGED is a regular hexagon.

So angle DBN = 540/5

=108°

and angle ABN = 180-108 = 72°.

since triangle ABN is isosceles therefore angle BAN=180-2x72°=36°.

let dotted line meets BN at point P. now angle PAN=36-18=18°.

So AP is bisect or of angle BAN.

further triangles BAP and NAP can be proved congruent easily and by cpct

angle BPA =angle NPA =

180/2=90°

also NP=BP=BN/2.

now in right triangle BAP,

sin 18°=BP/AB

=(BN/2)/r, or, 0.31=BN/2r and finally we get

answer BN=0.62r.