Assignment:
Problems:
1. Use superposition to find an expression for the current I in the network below. The angulare frequency of the AC source is ω = 1000 rad/s. Write a time dependent expression for the current I. (Note that one of the voltage sources is a DC source!).
2. Use node voltage analysis to determine the nodal voltages for the network below.
3. Write the branch current equations for the network below using the defined brunch currents. Do not solve for the currents. (Recall that branch current analysis involves writing KVL equations around each of the three loops of the circuit).
4. The network below is an equivalent model of a Single-Phase, Capacitor-Run. motor. This is a special type of single phase motor which is capable of delivering a constant torque from a single phase solute. The stator of the motor is made up of two coils and a capacitor. The main coil is made from a thick wire to reduce resistance and has a large number of turns to increase impedance. The auxiliary coil is made from a thin wire to increase resistance and has a small number of turns to reduce impedance. The ring shaped component is a squirrel cage rotor, it reacts to the changing magnetic fields (Φm and Φα) by spinning.
(a) Calculate the main and auxiliary currents Im and Iα.
(b) Accurately sketch a phesor diagram showing Vs, Is, and Ia.
(c) Calculate the real and reactive power supplied by the voltage source.
