A uniform wire of resistance `9 Omega` is cut into 3 equal parts. They are connected in form of equilateral triangle `ABC`. A cell of e.m.f. `2V` and negligible internal resistance is connected across `B` and `C`. Potential difference across `AB` is

Options

A. `1 V`
B. `2 V`
C. `3 V`
D. `0.5 V`

Answer

A

Explanation

(a) The circuit can be drawn as follows
Equivalent resistance `R = (3 xx (3 + 3))/(3 + (3 + 3)) = 2 Omega`
Current `i= (2)/(2) = 1A`. So, `i_(1) = 1 xx ((3)/(3 + 6)) = (1)/(3) A`.
Potential difference between `A` and `B = (1)/(3) xx 3 = 1` volt