question_answer

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

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 paths AD, DB and DC are in the ratio of \[1:2:3\]

D)  currents in the paths AB, DB and DC are in the ratio of \[3:2:1\]

Correct Answer: C

Solution :

Applying Kirchhoff’s law at point D, we get                 \[{{I}_{1}}={{I}_{2}}+{{I}_{3}}\]                 \[\frac{{{V}_{A}}-{{V}_{D}}}{10}=\frac{{{V}_{D}}-0}{20}+\frac{{{V}_{D}}-{{V}_{C}}}{30}\] or            \[70-{{V}_{D}}=\frac{{{V}_{D}}}{2}+\frac{{{V}_{D}}-10}{3}\] \[\Rightarrow \]               \[{{V}_{D}}=40\,\,V\] \[\Rightarrow \]               \[{{i}_{1}}=\frac{70-40}{10}=3\,A\]