Accounting for Charge

Chapter 19

Objectives Understand charge and energy

conservation in electrical circuits Apply Kirchoff's Current and Voltage Laws Find equivalent resistances Understand the concept of charge carrier

Accounting for Charge (q) Charge is a property of elementary particles

such as Electrons: q = -1, and Quarks: q = +2/3 or q = -1/3

Combinations of quarks yield: Protons: q = +1 = (2/3) + (2/3) + (-1/3) Neutrons: q = 0 = (2/3) + (-1/3) + (-1/3), and several others combinations of 2 and 3 quarks

Protons and neutrons can be considered elementary particles in our analysis so we can forget about quarks in the rest of the chapter

Because each type of elementary particles always carries the same amount of elementary charge, the total charge for a group of elementary particles is an extensive quantity.

Certainly, the UAE is applied to each of these particles independently and so to their charges

UAE for Elementary Chargesq+

final - q+initial = q+

in - q+out + q+

gen - q+cons

q-final - q-

initial = q-in - q-

out + q-gen - q-

cons

To some extent, we can assume that the net charge in the universe is zero and that generation and consumption of +ve and –ve charges is concerted, i.e.,

However, the mass of the particle that carries the +ve charge is different to the mass of the particle that carries the –ve charge

q+gen= q-

gen q+

cons = q-cons

UAE for elementary charges without energy-mass transformationsq+

final - q+initial = q+

in - q+out + q+

gen - q+cons

q-final - q-

initial = q-in - q-

out + q-gen - q-

cons

0 0

0 0

UAE for net positive charge (General)

Defining...

qnet,+ q+ - q-

Subtracting Equation (1) from (2), we get: ,,,, net

outnetin

netinitial

netfinal qqqq

Defining...

qnet,- q- - q+

Subtracting Equation (1) from (2), we get:

,,,, netin

netin

netinitial

netfinal qqqq

UAE for net negative charge (General)

Pairs Problem #12 mol of hydrogen (H2) and 1 mol of oxygen

(O2) are placed in a reactor. All of the hydrogen and oxygen react to form water. Initially how many moles of positive charge

are in the reactor? Negative? Net positive? After the reaction, how many moles of

positive charge are in the reactor? Negative? Net positive?

BatteriesA battery produces electricity (flow of

electrons) from a chemical reaction. Primary battery: once the reactants are

consumed, the battery is dead Secondary battery: can be recharged

Example: Lead-Acid Battery DischargingAnode and cathode immersed in sulfuric acid

Anode (-) made of lead (Pb) Cathode (+) made of lead oxide (PbO2)

(cathode) OH2PbSO2H3HSOPbO

(anode) 2HPbSO HSO Pb

24-42

4-4

e

e

Charging the Battery These reactions go the opposite direction

when the battery is being charged. Some lead sulfate falls to the bottom of the

container instead of collecting on the anode and cathode. Thus, the battery cannot be exactly 100%

charged and will eventually have to be replaced.

Lead-Acid Battery ChargingAnode and cathode immersed in sulfuric acid

Anode (-) made of lead (Pb) Cathode (+) made of lead oxide (PbO2)

(cathode) OH2PbSO2H3HSOPbO

(anode) 2HPbSO HSO Pb

24-42

4-4

e

e

ResistorsResistors: passive devices that consume electrical

energy. They oppose to the pass of electrons

parallelseries

Current is the same in resistors in seriesVoltage is the same in resistors in parallel

Voltage is divide by resistors in seriesCurrent is divided by resistors in parallel

Electrical circuit is a network consisting of a closed loop containing power sources (current or voltage) and devices such as resistors

Electric Circuits

V+

-

2i

3i1i

3i1i

2i

An example of a voltage source is a battery; ideally it should produce a voltage independent of the current

An example of a current source is a specialized transistor circuit, which should provide a current independent of the voltage.

Remember i = q/t and v = E/q Assume the wires have R = 0 and V

has not internal resistance

i2 = i1 + i3

By convention: A current is positive when goes in the opposite direction of the negative carriers or in the direction of the positive ones

Kirchoff’s Laws Net current at each node is zero (charge

conservation) Net voltage in each loop is zero (energy

conservation)

Circuit Analysis

V+

-

1i 3i

2i

32

32

321

33

22

321

11

,

RR

RRV

RRVi

R

Vi

R

Vi

iii

ii outin

R2 R3

Resistors in Parallel Resistors in parallel can be combined to form the

equivalent resistance

V+

-Req

k keq RR

11

i

V+

-R1 R2 R3

i

i1 i2 i3

Resistors in Series Resistors in series can also be combined

k

keq RR

V+

-

R1

R2

R3

i

V+

-Req

i

Pairs Exercise #2Find the equivalent resistance and the total

current in the circuit below.

5 V+

-

4 k 4 k 2 k

i

i1 i2 i3