In the network shown in fig. , points A, B, and C are at potentials of 70 V, 0, and 10V, respectively.

Options

A. The point `D` will be at a potential of `60 V`
B. The point `D` will be at a potential of `20 V`
C. Current in the paths `AD, DB` and `DC` are in the ratio `1 : 2: 3`
D. Current in the paths `AD, DB` and `DC` are in the ratio `3 : 2 : 1`

Answer

D

Explanation

`V_A - V_D = ixx 10 rArr 70 - V_D = 10 i` …(i)
`V_D - V_B = i_1 xx 20 rArr V_D - 0 = 20 i_1` …(ii)
`V_D - V_C = (i-i_1) xx 30 rArr V_D - 10 = 30 (i- i_1)`…(iii)
From (i) and (ii)
`70 - 20 i_1 = 10 i rArr i + 2 i_1 = 7`....(a)
From (ii) and (iii)
`20 i_1 - 10 = 30 (i - i_1) rArr 3 i- 5 i_1 = -1` ...(b)
Solving (a) and (b)
`i_1 = 2 A, i= 3 A, i - i_1 = 1 A`
`V_D = 20 i_1 = 40 V`
`i : i_1 : (i - i_1) = 3 : 2 : 1`.