Overview of ENGR 220 Circuits 1

1. Overview of ENGR 220Circuits 1 Fall 2005 Harding University Jonathan White

2. Sections • Basic Concepts • Resistive Circuits • Capacitors/Inductors • RC, RL, and RLC circuits • OP Amps • Intro. to AC Circuits

3. Basic Concepts • Charge – electrical property of matter that exists because of an excess or deficiency of electrons • Current – rate of flow of charge (electrons) • Voltage – amount of energy available to move electrons from one point to another in a circuit • Energy – fundamental capacity to do work • Power – rate of energy usage • Electron shells / Valence electrons / Conductors/Semiconductors/Insulators / Circuit symbols

4. Basic Concept Questions • How many coulombs of charge do 50 x 1031 electrons possess? • 500 joules of energy are used to move 100 C of charge through a resistor. What’s the voltage across the resistor? • How much energy does a 12 V battery in your car use to move 2.5 C through the electrical circuit? • .6 C passes a point in 3 s. What’s the current in amperes?

5. Resistive Circuits – Basic Laws • Resistor – Device that opposes the flow of current • Ohm’s Law: v = iR • Kirchoff’s voltage law: Sum of voltages around a closed loop is zero • Kirchoff’s current law: Sum of currents entering a node is equal to the currents leaving a node • Parallel resistors: Req= (R1R2) / (R1 + R2) • Series resistors: Req= (R1 + R2) • Power: P = I2R, P = VI, P = V / I

6. Basic Law Questions • In the circuit below, what’s V1 and V2 ?

7. Resistive Circuits - Analysis • Nodal Analysis - Choose a node; setup current and voltage equations using KCL and Ohm’s Law; solve for unknown voltages • Mesh Analysis – Find all loops; setup variables as the unknown mesh currents; apply KVL to each loop; solve for the unknown voltages.

8. Resistive Circuits – Analysis Questions • Using mesh current analysis, determine the current through RL if Vsource = 5V, R1=R2=10 KΩ, R3=R4=5 KΩ, R5=RL=2 KΩ ?

9. Resistive Circuits – Other topics • Superposition – Method of analyzing circuits with 2 or more independent sources by examining effects of each source by itself and then combing the effects. • Thevenin’s Theorem: A 2 terminal circuit can be reduced to a voltage source in series with an equivalent resistance. • Norton’s Theorem: A 2 terminal circuit can be reduced to a current source in parallel with an equivalent resistance.

10. Resistive Circuits – Other Topics Questions • Find the Thevenin equivalent with respect to the 3K resistor.

11. Capacitors • Capacitor – Device that stores charge. • Physically, 2 conductive plates that are very close to each other but not touching • Capacitance: C = Q / V • Current through a capacitor: I = C (dv / dt) • Series capacitors: Ceq = (C1C2) / (C1 + C2) • Parallel capacitors : Ceq = (C1 + C2) • Just the opposite of resistors • Acts like an open circuit to dc.

12. Inductors • Device that stores energy in its magnetic field. Resists changes in current by inducing a voltage to oppose the change in current. • Physically: Coil of wire wrapped around a conductive material. • Voltage through an inductor: v = L (di / dt) • Series and Parallel Inductors: Like resistors. • Acts like a short circuit to dc.

13. Capacitor/Inductor Questions • What’s the equivalent capacitance of the circuit below?

14. Combinations of Resistors, Inductors, and Capacitors • What is the step response of the circuit below?

15. OP Amps • Takes an input and produces a desired output. • OP Amp – Can be designed to perform mathematical operations such as addition, subtraction, multiplication, division, differentiation, and integration. • Basis for analog computers

16. OP Amp Questions • What is Vo equal to in the circuit below?

17. AC Circuits Introduction • Sine waves, frequency, period • RMS values of voltage • Angular measurement of sine waves • Equation for sine waves • Non sinusoidal waveforms