CIRCUITSUnit 11

History: The Electric Battery When was electricity first

recognized? By Benjamin Franklin with his famous

kite experiment in 1752. It wasn’t until almost 50 years later, in

1800 when Alessandro Volta invented the electric battery.

History: Galvani Luigi Galvani (1737-1798) was a professor at

the University of Bologna He carried out a long series of experiments on the

contraction of frog leg muscles through electricity He found that contraction of the muscle could

also occur when the frog was hung by a brass hook and then touched by an iron railing

He hypothesized that the source of the charge came from the frog’s leg muscle itself

He termed this “animal electricity” and many scientists thought he had discovered the “life-source”

Current: Volta Though Alessandro Volta continued many of

Galvani’s experiments and expanded on them, he was skeptical of this “animal electricity”

Volta came to realize that the charge came from contact between two metals and not within the animal itself

Discovered when he placed a salt solution or dilute acid between two metals and stacked them on top of one another, he created a greatly increased potential difference This was the first battery ever made

Battery Batteries contain two plates of different

metals called electrodes The electrodes are immersed in a

solution called the electrolyte If the cell is a dry cell the electrolyte is

immersed in a powdery paste

Electric Current When a continuous conducting path is

connected between terminals of a battery we have an electric circuit

Electric Current Electric current is the net charge that

passes through a point per unit time I = ΔQ

t I = current Q = charge t = time

The unit of current is called the ampere (A)

Question: pg 531 A steady current of 2.5 A flows in a

wire for 4.0 min. The charge on an electron is 1.6 x 10-19 C/electron. a) How much charge passed through any point in the circuit?

b) How many electrons would this be?

Current Specifics

The direction of current flow from the positive to the negative terminal.

Electrons actually flow from the negative to the positive terminal.

This is the OPPOSITE of conventional current.

Conventional Current Electron Flow

Resistance & Ohm’s Law Georg Simon Ohm (1787-1854)

established that current in a metal wire is proportional to voltage. I α V

Current depends not only on voltage, but also on the resistance of the wire.

The higher the resistance the less current that will flow through a wire for a given voltage.

Ohm’s Law: V = IR

Question: pg 533 A small flashlight bulb draws 300

mA from its 1.5-V battery.

A) What is the resistant of the bulb?

B) If the voltage dropped to a 1.2 V, how would the current change?

Measuring DevicesAn amnmeter is used to measure current (A)

A voltmeter is used to measure voltage (V)

An ohmeter is used to measure resistance (Ω)

Resistivity The internal resistance of a wire can be

related to the wire’s length and cross-sectional area by the equation:

R = ρL A

ρis measure of the resistivity of a wire. This is dependent on the type of metal used in the wire and is a constant value.

Question: pg535 Suppose you want to connect your

stereo to remote speakers. A) If each wire must be 20 m long, what

diameter copper wire should you use to keep the resistance less than 0.10Ω per wire?

B) If the current to each speaker is 4.0 A, what is the voltage drop across each wire?

Power Electrical energy is useful to us because we

can easily transform it into other forms of energy.

We can measure electrical power, which tells of the RATE of energy transformed over time: P = energy transformed = QV

time t Also:

P = IV P= I2R P= V2

R

Question

Question: pg539An electric heater draws 15.0 A on a 120-V line. How much power does it use and how much does it cost per month (30 days) if it operates 3.0 h per day and the electric company charges 10.5 cents per kWh?

Resistors in Series A resistor is a part of a circuit used to

control the amount of current flowing through parts of a circuit

When resistors are connected end to end as shown below, resistors are said to be in series

Resistors in Series To calculate the value of resistance in

series you just add up the total value: Rtotal : R1 + R2 + R3 + …

Resistors in Parallel When the current in a circuit splits over

2 resistors, the resistors are said to be in parallel

Resistors in Parallel To calculate resistors in parallel: 1 = 1 + 1 + 1 + … Rtot R1 R2 R3

Question: pg 558 The light bulbs below are identical and

have resistance R. Which configuration produces more light? Which way do you think headlights are wired?

Combined Circuits Practice

Combined Circuits Practice

Combined Circuits Practice

Voltage Drops Across Individual Resistors

Individual Resistors

Rechargeable Batteries•"One of the necessary conditions for a battery to be rechargeable is that the underlying chemical changes that occur during an electrical discharge from the cell must be efficiently reversed when an opposite electrical potential is applied across the cell. •In nickel-cadmium (NiCad) batteries, for example, the Cd(OH)2 and Ni(OH)2 that are formed during cell discharge are readily converted back to the original electrode materials (Cd and NiOOH), when the cell is recharged•To be classified as rechargeable, the battery must be able to undergo the reverse reaction efficiently, so that hundreds or even thousands of recharging cycles are possible.

Lithium Ion Batteries•During discharge, lithium ions Li+ carry the current from the negative to the positive electrode, through the non-aqueous electrolyte and separator diaphragm.[8]

•During charging, an external electrical power source (the charging circuit) applies a higher voltage (but of the same polarity) than that produced by the battery, forcing the current to pass in the reverse direction. The lithium ions then migrate from the positive to the negative electrode, where they become embedded in the porous electrode material in a process known as intercalation

Why Do Batteries Die•Since there is a limit to how much chemical energy even the largest battery can hold, all batteries will "run out of juice" at some point. When the oxidation-reduction reaction that takes place inside your battery has completed, you have two options. First, if your battery is rechargeable, you can reverse the chemical reaction by recharging your battery. Second, if your battery is not rechargeable, you must dispose of it in the proper way. •Eventually, even rechargeable batteries will no longer be able to reverse their inner chemical reaction. The number of times a battery can be recharged varies according to the type of battery. Furthermore, batteries can lose their power when not in use. This is called "self-discharge," and it is caused by internal chemical processes that drain power almost as if the battery was attached to a small power-draining device.

Sherlock Holmes Question•It was a 19th century taser.Although they didn't really exist back then, tasers are basically just capacitors that store charge and then quickly release it when it touches a conductor. And capacitors did exist back then (although they were called condensers).•Induction coils of the time could easily generate 100,000 Volts.•Mainly, I think it was just to show that they were experimenting with electricity to justify the radio controlled device they made...which is also based on experiments that were just beginning to go on in that time period.

1986 B3

In the circuit shown above, X, Y. and Z represent three light bulbs, each rated at 60 watts, 120 volts. Assume that the resistances of the bulbs are constant and do not depend on the current.

a. What is the resistance of each bulb? b. What is the equivalent resistance of the three light bulbs

when arranged as shown? c. What is the total power dissipation of this combination

when connected to a 120‑volt source as shown?

1986 B3

In the circuit shown above, X, Y. and Z represent three light bulbs, each rated at 60 watts, 120 volts. Assume that the resistances of the bulbs are constant and do not depend on the current.

d. What is the current in bulb X ? e. What is the potential difference across bulb X ? f. What is the potential difference across bulb Z ?

EMF Any device that transforms one type of

energy to electrical energy is called a source of electromotive fore or EMF.

Parking Lot: Gatorade Battery?

First, let's examine the idea of powering any electronic device with a fruit or vegetable. The concept is believable because you can create a battery with a few potatoes. This experiment is a science class favorite because it helps demonstrate how the galvanic cells that make up a car battery work.

Some batteries use galvanic cells to transfer chemical energy into electric energy. They depend on two metals, a cathode or positive terminal (such as

copper) and an anode or negative terminal (such as zinc). These are placed in an electrically conductive solution that allows ions to

travel freely between the two metals. The solution is typically an acid. Car batteries use sulfuric acid, but potatoes contain phosphoric acid, which also works. The acid steadily eats away at the zinc, a chemical reaction that releases spare zinc electrons.

These electrons then join with spare hydrogen ions in the acid to create hydrogen gas.

Parking Lot: Lightning Harvest

There are a number of problems with trying to harness the tremendous energy of lightning bolts:

The first is that lightning is highly unpredictable. There is no way to know exactly where and when lightning will strike, so it would be difficult to find a location to turn into a facility for processing lightning for energy.

Lightning also delivers its energy all at once, which would require huge batteries and capacitors. Otherwise, the energy would simply blow out any systems established to capture it.

Parking Lot: Lightning Harvest

The potential instability in the supply of electricity from lightning is far less of an issue than the infrastructure which would be needed to support the energy collection process.

Lightning is so powerful that it would overload all but the most sophisticated and heavy-duty systems, and the wisdom of building and installing such a system would be questionable if it could only harvest the energy from a few lightning bolts a year.

Even in areas where lightning is frequent, the cost of the system would probably outweigh the benefit of getting electricity from lightning.

Parking Lot How can you level the measure of

awesomeness a person has? There’s an app for that! Description:

Have fun playing pranks on your friends with the Awesomeness Meter. It measures how Awesome you are by scanning your finger. Only you control the Awesomeness.

Parking Lot Pronunciation The Italian alphabet is fairly similar to our own

(English, or depending on where you're from, American). The letters K,J,W,X,Y occur only in foreign origin words. Each lesson will explain a few more letters. This week, I'll explain the interesting letters (or combinations thereof) from this week's words (above).

gn The gn is the same sound as Spanish ñ i.e. is the same

sound as the ny pair in the word canyon. Thus, signore is pronounced like sin-yore.

Internal Resistance Since we live in a not-so-perfect world, the

batteries that we use internally “steal” power from the actual voltage of the battery. This is called internal resistance.

When a battery is cited to have internal resistance, we can figure out how much actual voltage, called the terminal voltage, will be given to the rest of the circuit:

Vab = ξ- Ir r = internal resistance

A circuit consists of battery A of emf A = 60 volts and Internal resistance rA = 3 ohms; battery B of emf B = 12 volts and internal resistance rB = 1 ohm; and four resistors connected as shown in the diagram above.

A) Calculate the current In the 2‑ohm resistor. B) Calculate the power dissapated In the 3‑ohm

resistor. C) Calculate the terminal voltage of battery B.

Free Response Practice: 1981 B4

Question: pg 563 A 9.0-V battery whose internal

resistance r is 0.50Ω is connected in the circuit shown. A) How much current is drawn from

the battery? B) What is the terminal voltage of the

battery? C) What is the current in the 6.0-Ω

resistor?

Kirchoff’s Rules

At any junction point, the sum of all currents entering the junction must equal the sum of all currents leaving the junction.

The sum of the changes in potential around any closed path of a circuit must be zero.

Kirchoff’s Junction Rule Kirchoff’s Loop Rule

Kirchoff’s Rules

Kirchoff’s Rule Question

Capacitors A capacitor uses two parallel metal

plates to store electric charge The amount of charge that each plate can

hold is represented by the formula Q = CeqV

Q is the charge on each plate Ceq is the equivalent capacitance of the

system V is the voltage across the plates

Capacitance is measured in the unit Farads (F)

Capacitors in Series Capacitors in series are like resistors in

parallel 1 = 1 + 1 + 1 + … Ceq C1 C2 C3

Capacitors in Parallel Capacitors in parallel are like resistors in

series Ceq = C1 + C2 + C3 + …

RC Circuits: Steady State Behavior A lot of the time we’ll find capacitors

connected to resistors with a battery This is called an RC Circuit When the switch of the circuit is closed,

electrons flow from the negative terminal of the battery to the upper plate of the capacitor

Electrons that are leftover in the circuit will also flow to the positive terminal of the battery

RC Circuits: Steady State Behavior V = ξ(1— e-t/RC ) The product of the resistance, R, times

the capacitance, C, is called the time constant, τ

RC Circuits: Steady StateBehavior When a capacitor discharges from it’s

full charge the equation can be modeled after:

V = V0 e-t/RC