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Node Voltage Example - Example Problem Find currents Ix I2...

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Example Problem. Find currents I x , I 2 , and I 3 . 20 6V 2 8 5 16 10 8V I X I 2 I 3 A B C We first examine the circuit and select the node at the bottom of the circuit diagram as the reference. We do this since there is one voltage source connected to this node as well as three resistors. We then identify the other essential nodes as A, B, and C. We also note that a voltage source connects nodes A and B so we cannot use Ohm's law to calculate the current in this voltage source. We will use the Unknown Current Method to compute the current through the 6V voltage source. (We note that this unknown current is I x which the problem is already asking us to find.) We write the equation for the currents leaving node A: ( ) 1) (Eq. 8 . 0 = I + V 15 . 0 or 10 8 = I + 10 V + 20 V : terms grouping and ng Substituti 8V. = V that observe We 0 = I + 8 + 2 V - V + 20 V x A x A A C X C A A We next focus on node B: ( ) 3) (Eq. 2.4 = V (0.2625) + V 0.15 2, Eq. and 1 Eq. Adding 2) (Eq. 1.6 = I - V (0.2625) or 0 = I - 5 8 - V + 16 V B A X B X B B We now deal with the constraint equation. We know that the voltage between nodes A and B will ALWAYS be 6V since a voltage source is connected between them. In fact, we can state this
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