In a certain electrical network, the three nodes A, B and C are each at a potential of 1.0 volt whil

Question

In a certain electrical network, the three nodes A, B and C are each at a potential of 1.0 volt while the node D is at a potential 2.0 volt. The potential at the Node O in volt is

Accepted Answer

[Key Concept: Kirchhoff's current law at a floating node makes its potential the conductance-weighted mean of its neighbours.]

Apply KCL at point O

$$\begin{matrix} & \frac{V_{A} - V_{O}}{10} + \frac{V_{B} - V_{O}}{10} + \frac{V_{C} - V_{O}}{10} + \frac{V_{D} - V_{O}}{10} = 0 \\ & V_{O} = \frac{V_{A} + V_{D} + V_{C} + V_{D}}{4} = \frac{5}{4}\text{~volt~} \end{matrix}$$

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