Question

Seven resistors, each of resistance 5Ω, are connected as shown in fig, The equivalent resistance between points A and B is.... 

(A) 1Ω 

(B) 7Ω 

(C) 35Ω 

(D) 49Ω

Answer 1

The correct option (B) 7Ω

Explanation:

The circuit can be redrawn as shown.

Let a battery of EMF E is connected as shown.

The current in various branches is as shown.

applying Kirchoff's low to ACDA, CBDC, ADBGFA,

5i₂ + 5i₃ – 10i₁ = 0  (1)

10(i₂ – i₃) – 5(i₁ + i₃) – i₃ = 0   (2)

10 i₁ + 5(i₁ + i₃) – E    (3)

from (1) & (2) i₂ = {(3i₁)/2} & i₃ = (i₁/2)

if R is effective resistance between A & B then

R = {E/(i₁ + i₂)} = {E/(i₁ + {(3i₁)/2})} = {(2E)/(5i₁)}

from eqn (3), E = 15i₁ + 5i₃

∴ E = 15i₁ + 5 × (i₁/2)

 E = (35/2)i₁

∴ R = [{2 × (35/2)i₁} / {5i₁}] = 7Ω