A current of 2A flows in a system as shown in the figure. The potential difference between A and B `(V_(A)-V_(B))` will be

Options

A. 1V
B. 2V
C. 3V
D. 4V

Answer

A

Explanation

Given : Resistances `R_(1) = 2 Omega`
`R_(2) = 3 Omega , R_(3) = 3 Omega and R_(4) = 2 Omega`
We know that resistances `2Omega` and `3Omega` (in the upper) arm are in series combination .
`:.` Their equivalent resistance
`(R_(4)) = 2 + 3 = 5 Omega`
Similarly, equivalent resistance of the lower arm `(R_(1)) = 3 + 2 = 5 Omega`
Since the equivalent resistance of both arms are equal,
`:.` Current flowing through the upper and lower arms will also be equal
`l_(1) = l_(2) = (2)/(2) = 1A `
We also know that potential difference between C and A
`(V_(c) - V_(A)) = l _(1) R_(1)`
`= 1 xx 2 = 2 V` .....(1)
Similarly, potential difference between C and B
` (V_(C) - V_(B)) = l_(2) R_(2) = 1 xx 3 `
= 3 V .....(2)
Subtracting equation (1) and from (2)
`V_(C) - V_(B) - (V_(C) - V_(A)) = 3 - 2 = 1V `