In the circuit given here, the points A,B and C are 70 V, zero, 10 V respectively . Then,

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. Currents in the path AD, DB and DC are in the ratio of 1 : 2 : 3
D. Currents in the paths AD,DB and DC are in the ratio of 3 : 2 : 1

Answer

D

Explanation

Let V be the potential at D and `I_(1)=I_(2)+I_(3)` at D
`therefore (70-V)/(10)=(V-0)/(20)+(V-10)/(30)`
`therefore 70-V=(V)/(2)+(V-10)/(3)`
`=(3V+2V-20)/(6)=(5V-20)/(6)`
`therefore 6(70-V)=5V- 20 therefore 420-6=5 V-20`
`therefore 11 V= 440 therefore V= 40 V`
Thus the point D is at a potential of 40 V.
`therefore I_(1)=(70-40)/(10)= 3 A, I_(2)=(40)/(20)=2`,
`I_(3)=(40-10)/(30)= 1A`
`therefore I_(1) : I_(2) : I_(3)= 3 : 2 : 1`