A network has reference node 0 and two further nodes 1 and 2

A network has reference node \(0\) and two further nodes \(1\) and \(2\). All phasors are cosine-referenced RMS phasors; constant phases are in degrees. The branches are as follows: - an independent voltage source \(10.0\angle 20.0^\circ\,\mathrm{V}\) from node \(1\) to node \(2\), with the positive terminal at node \(1\), so that \(\mathbf{V}_1-\mathbf{V}_2=10.0\angle 20.0^\circ\,\mathrm{V}\); - a \(5.00\,\Omega\) resistor from \(1\) to \(0\); - a \(j8.00\,\Omega\) inductor from \(1\) to \(0\); - a \(4.00\,\Omega\) resistor from \(2\) to \(0\); - a \(-j6.00\,\Omega\) capacitor from \(2\) to \(0\); - an independent current source \(1.50\angle 0^\circ\,\mathrm{A}\) injects into node \(1\) from \(0\). No other element joins node \(1\) to node \(2\). Node voltages are with respect to \(0\). (a) Write the supernode constraint and the supernode KCL equation. (b) Solve for \(\mathbf{V}_1\) and \(\mathbf{V}_2\). (c) Determine the RMS current phasor through the voltage source, directed from node \(1\) towards node \(2\). Using the passive sign convention, compute the complex power of the voltage source and state whether that source delivers or absorbs average power. (d) Determine the complex power of the current source under the passive sign convention (the current-source current entering its marked-positive voltage terminal at node \(1\)).

A floating voltage source between two non-reference nodes forces a supernode.