Compute the value of current I flowing via the battery using ‘Node voltage’ technique

Solution:

All nodes are pointed in the figure above and ‘Node-g’ is chosen as the reference voltage. When a voltage source is associated directly among the two nodes, the current flowing via the voltage source cannot be established directly as the source voltage Vs is independent of the current. More to note that the source voltage Vs fixes the voltage among the nodes only. For the current illustration, the voltage of the central node is known as it is equivalent to (V_a – 10) volt.

KCL equation at node-a is as follows:

KCL equation at node-b is as follows:

To resolve the above equations, we require one more equation which can be acquired by applying the KCL at the central node (i.e. note central node voltage is (Va – 10) volt.

Repalcing the current expression in above equations we acquire,

The equations can be resolved to find V_b =50.43 and V_a =16.99 V. We can now refer to original circuit (figure above) to find directly the voltage across every element and the current via every element. The value of current flowing via the voltage source can be calculated by using the equation and it is given by I = 1.307 A. Note that the current I (+ve) is entering via the positive terminal of the voltage source and this points out that the voltage source is absorbing the power, in another words this case is observed whenever charging a battery or source.