CBSE Class 12-science Answered

When 12 Ω resistance is not connected in parallel to S than we can write,

Where l₁ = 40 cm.

Therefore, R = S (40/60) = (2/3)S………………..(i)

When 12 is connected in parallel to S, then

The effective resistance can be written as

1/S₁ = 1/S + 1/12 = (12+S)/12S

i.e. S₁ = 12S/(12+S)

Now we can write,

Where i' = 50 cm.

i.e.R = 12S/(12 + S) (50/50)= 12S/(12 + S) …………..(ii)

Now using (i) and (ii) we get,

(2/3)S = 12S/(12 + S)

S = 6 Ω

Therefore from (i), R = (2/3) (6) = 4 Ω.