Homework 2

Due at 11:59pm on Thursday, April 16th. Submit to https://canvas.uw.edu/courses/1883403/assignments/11376146 . It is fine to submit scanned or a picture of handwritten answers, but we must be able to read it. Indicate your final answer clearly, show your work. Each problem is 10 points (all subproblems weighted equally).

Problem 1

Consider the following circuit:

Find

a) The power (active and reactive) delivered to the load.

b) The power (active and reactive) coming out of the source.

Problem 2

Consider the circuit shown above.

a) Suppose we want to achive unity power factor at the load (that is, a power factor of 1) by adding a capacitor in parallel. Find the size of the capacitor (in unit of \(\Omega\)).

b) Now we want to tune the capacitor such that the source to only delievers active power. Is it possible? Explain why or why not.

Problem 3

Consider a load supplied by a \(120V (rms)\) AC source. The load is a \(1 \ \Omega\) resistance in parallel with a \(100 \ mH\) inductor. Find

a) Active power delivered to the load in North America

b) Active power delivered to the load in Europe

Problem 4

A voltage source \(V = 220\angle120^\circ\) is connected across a load consisting of a \(15\ \Omega\) resistance in series with a \(100\ \mu\text{F}\) capacitance. Assume the circuit is energized in the United States.

(a) The load power factor

(b) The reactive power consumed by the load

Problem 5

An electric load consists of a \(15\ \Omega\) resistance in series with a \(10\ \Omega\) inductive reactance. The load is connected in parallel with another load of unknown impedance. The voltage source of the system is \(220\ \text{V}\). The total real and reactive powers delivered by the source are \(4\ \text{kW}\) and \(2\ \text{kVAR}\), respectively. Compute the impedance of the unknown load. State the real and reactive components.

Problem 6

A \(630\ \text{V}\) AC voltage source is connected to two parallel connected impedances. One impedance draws \(10 + j15\ \text{kVA}\), and the other impedance draws \(15 - j10\ \text{kVA}\).

a) Find the source current.

b) A capacitor is added in parallel such that the source delievers power at unity power factor. Find the value of the capacitor (in \(\Omega\)).

Problem 7

A buck converter has a source voltage \(V_s = 15\ \text{V}\) and a load resistance \(R = 15\ \Omega\). If the duty ratio of the transistor is \(60\%\), compute the following:

a) Voltage across the load

b) Power delieved to the load

Problem 8

A boost converter has a source voltage \(V_s = 10\ \text{V}\) and a load resistance \(R = 2\ \Omega\). If the duty ratio of the transistor is \(50\%\), compute the following:

a) Voltage across the load

b) Power delieved by the source

Problem 9

A boost converter is used to step up \(30\ \text{V}\) to \(50\ \text{V}\). The switching frequency of the transistor is \(5\ \text{kHz}\), and the load resistance is \(25\ \Omega\). Compute the following:

(a) The current ripple when the inductor is \(L = 7.5\ \text{mH}\)

(b) The average current of the load