Final answer:
The question involves Engineering, where nodal analysis is used to find voltages at circuit nodes and to calculate power delivered by a dependent source, using principles like Kirchhoff's current law and Ohm's law.
Step-by-step explanation:
The subject of this question is Engineering, specifically electrical engineering where nodal analysis is used as a method to determine voltages in a circuit and calculate power. To solve for the voltage across specified nodes, you apply Kirchhoff's current law (KCL) at each node, setting up equations based on the sum of currents entering and leaving the node. Once the node voltages are determined, Ohm's law (V=IR) can be used to determine the current through each resistor.
To calculate the power delivered by the dependent source, the power is calculated as P=IV where 'I' is the current through the source and 'V' is the voltage across it. For resistors, power can be calculated using P=V2/R where 'V' is the voltage drop across the resistor. Checking the power dissipation against the power supplied by the sources in a circuit is not only a good practice for verification but also significant for an understanding of the conservation of energy in electrical circuits.
At the end of the process, ensuring that the total power delivered by the sources is equal to the sum of the powers dissipated by the resistors and the power consumed by the dependent source validates the nodal analysis calculations, thus underlining the significance of power considerations in circuit analysis.