The circuit of Figure P8-71 emulates a typical 60-Hz residential power system. There are three wires entering the house, two are called "hot" and the remaining one is called the return or "neutral." Each hot line is protected by a circuit breaker-but not the return. In the "house," appliances such as lights, toasters, and electronics are connected between one of the hot wires and the neutral. Large appliances such as ovens and dryers are connected between the two hot wires. Appliances are designed to operate with either \(120 \mathrm{~V}\) or \(240 \mathrm{~V}\) within a few volts either way.

(a) Show that if \(R_{1}\) and \(R_{2}\) are equal, \(\mathbf{I}_{\mathrm{N}}=0\) and \(\mathbf{V}_{1}=\mathbf{V}_{2}\).

(b) Consider a typical power draw where an \(R_{1}\) is, for example, a 130- \(\Omega\) light bulb, \(R_{2}\) a 40- \(\Omega\) toaster, and \(R_{3} 10-\)\(\Omega\) clothes dryer. Find the phasors \(\mathbf{V}_{1}\) and \(\mathbf{V}_{2}\) and find \(\mathbf{I}_{N}\).

(c) Based on your results in (a) and (b), is the neutral line even necessary? Open the neutral line, that is, force \(\mathbf{I}_{\mathrm{N}}=\mathrm{O}\), and again find the voltages \(\mathbf{V}_{1}\) and \(\mathbf{V}_{2}\). What is your answer? Would your home be better protected by adding a breaker to the return line?

(d) Simulate the circuit in Multisim and validate your results. The source frequency is \(60 \mathrm{~Hz}\).