Question

The network is made of uniform wire. The resistance of portion EL is 2Ω. Find the resistance of star between points F & C. 

(A) 0.985Ω 

(B) 1.25Ω 

(C) 1.946Ω 

(D) 1.485Ω

Answer 1

The correct option (C) 1.946Ω  

Explanation:

Consider triangle CHK. by property of triangle,

{R/(sin36)} = {r/(sin72)} ⇒ R = {r/(2cos36)} = 0.62r, r = 2Ω

Now given network can be redrawn as shown in fig. (b). Which can be turthes simplified to figure (c).

Circuit in (c) is wheat stone’s bridge. Hence in balanced condition, circuit is equivalent to combination of r + 0.946r = 1.946r joined in parallel with other 1.946r between C and F.

∴ Resistance of star between F & C is

R_FC  = {(R₁R₂)/(R₁ + R₂)}

= {(1.946r × 1.946r)/(2 × 1.946r)}

= {(1.946r)/2}

= {(1.946 × 2)/2}

= 1.946Ω