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LECTURE REVIEW OF BASIC CIRCUITS CONCEPTS

- September 28, 2009

REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL

QUANTITIS

Charge, Current, and Voltage

REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL

QUANTITIS

- Charge is measured in coulombs .
- Current is a flow of electrical charge from one

region to another. - Currents not only have magnitude, but also have

direction. - To indicate its direction, a current is described

by a number with a sign.

REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL

QUANTITIS

Current in a wire has its value and the

reference direction (direction of the arrow).

Choice of the reference direction is

arbitrary. By definition, a current is positive

when positive charges move in the reference

direction. If I is a negative number, this

means that current flows in the direction

opposite to the direction of the arrow.

REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL

QUANTITIS

- Electrical Potential and Voltage
- When electrical forces act on a charged particle,

it will possess potential energy the value of it

depends on the particle location. - The potential energy can be turn into kinetic

energy by releasing the particle. - After a while the particle will reach a position

where its potential energy is lower, and the

potential energy difference will be converted to

kinetic energy.

REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL

QUANTITIS

- To describe the potential energy that a particle

with a charge will have at point , the

electric potential is defined as - where is the potential energy of the

particle with charge at the position . - IMPORTANT The zero point of potential energy can

be arbitrarily chosen. The reason for this is

that only differences in potential energy have

practical meaning.

REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL

QUANTITIS

- We can choose any point in a circuit to be the

point where electrical potential is zero. This

point is referred as the ground point. - Just as with potential energy, it is the

differences of electrical potential that matter.

- The term voltage is used for difference in

electric potential. - Voltages can either positive or negative numbers

and are measured in volts ( ). It is usual to

express all potentials with respect to the

ground. - The potential difference between any point and

ground is called the voltage at that point. The

words voltage at point A always mean the

potential at point A with respect to ground. The

symbol for this voltage is .

REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL

QUANTITIS

If there is a circuit element with voltage

indication with and signs, that means that

the indicated voltage is equal to the potential

at the sign minus the potential at the sign.

REVIEW OF BASIC CIRCUITS CONCEPTS Problem

(the potential at A with respect to the ground)

is 4V. And

?

What is

PROBLEM

In Fig. (a), the current I1 is -2mA. Is it

possible to say what I2 is and why?

In Fig. (b), the current I1 is 2mA. Is it

possible to say what I2 is and why?

Is it possible to say what I3 is and why?

REVIEW OF BASIC CIRCUITS CONCEPTS

- Circuit elements Wires, voltage sources, current

sources, resistors, capacitors, inductors, - We will assume that wires are ideal (perfect

conductors) and all points along a wire are at

exactly the same potential. - Open circuit exists between two points when they

are not connected together by any circuit

element. No current can flow through the open

circuit. - Short circuit exists between two points when they

are connected together by an ideal wire. Both

points have the same voltage. - Additional terms Nodes and loops.

REVIEW OF BASIC CIRCUITS CONCEPTS KIRCHHOFFS LAWS

- KCL The algebraic sum of the currents entering

and leaving - a junction is zero
- KVL The algebraic sum of the changes in

potential around a - closed loop is zero

I2

I1

I1I2I3

I3

http//www.rfcafe.com/references/electrical/kirchh

offs_law.htm

b

c

0(Vb-Va)(Vc-Vb)(Vd-Vc)(Va-Vd)

a

d

REVIEW OF BASIC CIRCUITS CONCEPTS DC CIRCUIT

ANALYSIS

- The circuit elements Ideal resistors, Ideal

voltage and current sources. - Ideal voltage source
- Ideal current source
- Ideal resistor is described by Ohms law
- The algebraic signs of voltage and current are

very important. - Useful First choose the reference direction for

current through the resistor. The value of this

current is the potential at the tail of the arrow

minus the potential at the head of the arrow,

divided by R. - Try memorizing this rule.

REVIEW OF BASIC CIRCUITS CONCEPTS DC CIRCUIT

ANALYSIS

- How we should choose a sign of each voltage in

the circuit? - KVL

As a result, KVL has the form

REVIEW OF BASIC CIRCUITS CONCEPTS RESISTORS IN

SERIES

- Two resistors in series

II1I2

V0V1V2

Ohms law for each element VIR

V0I1R1I2R2 Ohms law for complete

circuit V0IReq

ReqR1R2

gt

It is the voltage that is divided between

elements in series.

REVIEW OF BASIC CIRCUITS CONCEPTS RESISTORS IN

PARALLEL

- Two resistors in parallel
- Resistors are connected in such a way that

they branch out from a single - node

VV1V2

II1I2

V/ReqV1/R1V2/R2

gt

1/Req1/R11/R2

It is the current that is divided between the

elements in parallel.

POWER IN RESISTORS

- The power dissipated by a resistor
- PIV or I2R
- Circuit is
- short if R0
- open if Rinfinity

REVIEW OF BASIC CIRCUITS CONCEPTS AC CIRCUIT

ANALYSIS

- Everything we have learned about DC analysis

remains true in the AC, or time-varying, case. - The circuit elements - ideal voltage sources,

current sources, and resistances - behave in the

same way whether or not the voltages vary in

time. - Additional elements that are useful only in AC

circuits capacitors and inductors. - Sometimes interaction of AC signals with

inductors and capacitors can provide striking

results How the very large voltages - tens kV -

can appear in the sparkplug in a car where power

is supplied by a battery of 12 V? - This amazing voltage transformation is usually

obtained by using a single inductor.

REVIEW OF BASIC CIRCUITS CONCEPTS IDEAL CAPACITOR

- Basic physics of the capacitor lies in the fact

that the voltage across the capacitor is linearly

proportional to the charge on its plates. - QCV gt IdQ/dtCdV/dt
- We have to specify algebraic signs. We will adopt

the same nomenclature used for resistances.

In dc circuits capacitors behave just like an

open circuit.

Just as with Ohms law, the algebraic signs of

the current and voltage are of greatest

importance.

CAPACITORS

- Two capacitors in parallel
- I C1dV/dt C2dV/dt (C1 C2)dV/dt
- Cpar C1 C2
- Two capacitors in series
- I C1dV1 /dt C2dV2 /dt
- dV/dt dV1 /dt dV2 /dt dV1 /dt C1/C2 dV1

/dt (1 C1/C2)dV1 /dt - dV1 /dt I/ C1 Cser C1 C2 /(C1 C2)

REVIEW OF BASIC CIRCUITS CONCEPTS IDEAL INDUCTOR

- The I-V relationship

If current through an inductor is constant, the

voltage across the inductor will be zero.

RC CIRCUITS, CHARGING CAPACITOR

For tlt0 switch was in position b and at t0 it

moved in position a.

KVL Vb-VR-VC0 VRIR ICdVC/dt

vR

Solution of non-homogeneous diff. eq-n is sum of

general solution of homogeneous equation and

particular solution of non-homogeneous equation.

Since Vbconst, particular solution is VConstVb

RC CIRCUITS, CHARGING CAPACITOR

At t0 V0 gt A -Vb

RC CIRCUITS, DISCHARGING CAPACITOR

For tlt0 switch was in position a and at t0 it

moved in position b.

KVL

VR

VR IR

At t0 VVbgt AVb

SUMMARY CHARGING AND DISCHARCHING A CAPACITOR