Electric Current

Unit 3

Batteries

• A battery is a device that produces electricity by transforming chemical energy into electrical energy.

• There are many types of batteries, but all operate on the same principle.

• We will examine the process behind a simple, wet-cell battery.

Batteries

• A simple battery consists of two rods of dissimilar metals, called electrodes, immersed in a solution called an electrolyte.

• One electrode may be constructed out of carbon.

• The part of the electrode not in contact with the electrolyte is called the terminal.

Batteries

• The sulfuric acid tends to dissolve the zinc electrode.

• Zinc atoms break off from the electrode and enter into solution with the acid.

• Each zinc atom that dissolves leaves behind two electrons on the electrode.

Batteries• As this process continues, the

zinc electrode becomes negatively charged.

• As the acid gains more positive zinc ions, electrons are pulled off of the carbon electrode, leaving it with a net positive charge.

• This charge difference leads to a potential difference between the two terminals.

Batteries

• If the terminals are not connected, only a little zinc is dissolved and the potential difference is held constant.

• If the terminals are connected (say, with a wire), charge can flow and more zinc must be dissolved to maintain the potential difference.

• This continues until the zinc electrode is completely dissolved.

• The battery is then “dead.”

Batteries

• The potential difference a battery can maintain depends on the materials the electrodes are made of.

• If two batteries are connected such that the positive terminal of one is connected to the negative terminal of the other, the batteries are connected in series.

• The voltages of two batteries connected in series add.

Electric Current

Electric Current

• The purpose of a battery is to create a potential difference (voltage).

• Voltages cause charges to move.

• When charges are moving, we say there is an electric current.

Electric Current

• More precisely, electric current is defined as the amount of charge that passes through the full cross section of wire in a small amount of time.

• Mathematically, this is

Electric Current

Amount of charge

Time interval

Electric Current

• Current is measured in coulombs per second (C/s).

• This unit is known as the ampere (A).

• Ampere is often abbreviated as just amp.

• Often, we will have currents much smaller than an ampere, usually on the order of a milliampere (mA) or a microampere (A).

Electric Current

• WARNING: Electric current can only flow when there is a continuous conducting path.

• This is called a complete circuit.

• If there is a break in the circuit, we call it a open circuit.

• If a circuit is complete, but has no load, it is called a short circuit.

Electric Current: An Analogy

Conclusion: Batteries do not create charge, lightbulbs do not

destroy charge.

Example: Current

A steady current of 2.5 A exists in a wire for 4 minutes.

a) How much total charge passed through a point in the circuit in this time?

b) How many electrons would this be?

Conventional Current

• When electric current was defined, it was assumed that positive charges were what was moving through the wire.

• As a result, electric current was defined to flow from the positive terminal to the negative terminal.

Conventional Current

• However, we know that electrons are the mobile charges in the circuit.

• As a result, charge actually flows from the negative terminal to the positive terminal.

• We still use the original definition of current, called the conventional current.

Homework

• Read sections 18-1 and 18-2.

• Do problems 1-3 all on page 515.

Resistance

Ohm’s “Law”

Current and Voltage

• We have learned that a voltage is needed to produce a current in a wire.

• It was discovered early on that the amount of current flowing through the wire is proportional to the voltage.

• So a 6 V battery produces twice the current of a 3 V through the same piece of wire.

Water Analogy Revisited

Resistance

• The current flowing through a wire depends not only on the size of the wire, but also on the resistance it offers to the flow of electrons.

• The greater the resistance, the less current for a given voltage.

• This relationship can be described mathematically:

Resistance

• R is called the resistance of the material.

• Notice that R and I are inversely related. As R increases, I decreases.

Ohm’s “Law”

• The equation for resistance is often written as

• This is known as Ohm’s law.• This is not a fundamental law of nature.• It is only true for a certain class of

materials (usually metals), where R is a constant and does not depend on voltage.

Ohm’s Law

• Materials that obey Ohm’s Law are called ohmic materials. Materials that do not are called nonohmic.

• Resistance is measured in V/A.

• This unit is called an ohm ()

Example

A small flashlight is powered by a 1.5 V battery. If the lightbulb draws 300 mA of current, what is the resistance of the bulb?

Suppose the battery begins to run low and the voltage drops to 1.2 V. What would be the new current in the circuit?

Resistors

• Any component of an electric circuit has a resistance to the flow of current.

• Wires generally have very low resistances, while items such as lightbulbs and heaters have much higher resistances.

Resistors

• We have already seen that the current through a circuit depends on the resistance.

• In electronics, resistors with known values of resistance are used to control the amount of current in the circuit.

Resistors

• Resistors can be found that range from less than an ohm to millions of ohms.

• On a circuit diagram, a resistor is represented with the symbol

Conceptual Example

A current I enters a resistor R as shown.

a) Is the potential higher at point A or point B?

b) Is the current greater at point A or point B?

Resistors

• In a circuit, the electric potential on one side of the resistor is greater than on the other.

• This makes sense, as energy is needed to push the current past the resistance.

• We say there is a voltage drop across the resistor.

Some Clarifications

• A battery maintains a constant voltage between its two terminals. It is a voltage source.

• Voltage is applied across a wire or circuit element. Voltage increases across a battery, and drops across a resistor.

Some Clarifications

• Electric current passes through a wire or circuit element.

• The amount of current that flows depends on the resistance of the device.

• Resistance is a property of the device. It does not depend on I or V.

Some Clarifications

• Conventional current flows from high potential (+) to low potential (-).

• Electrons actually flow in the opposite direction of the conventional current.

• Current and charge do not increase, decreased, or get used up. The amount of charge that goes into one end of the circuit comes out the other.

Homework

• Read 18-3.

• Do problems 5, 7, and 9 on pages 515-516.

Resistivity

Resistivity

• We learned yesterday that resistance is a property of the material.

• Scientists quickly asked what aspects of the material determine its resistance to electric current.

Resistivity

• Through experiments, scientists determined that resistance was directly proportional to the length of the resistor.

• They also determined that it was inversely proportional to the cross-sectional area of the resistor.

L

A

Resistivity

• Mathematically, this is described in the relationship

• The constant (rho) is known as the resistivity of the material.

• Resistivity is measured in units of m, and its value depends on the material.

Resistivity• We generally look up resistivity in a table.• Lower values indicate lower resistances.

Example: Speaker WiresYou are setting up your speakers for your stereo system. In order to get the optimal sound, you want the wires (made of copper) to each have a resistance of no more than 0.10 .

a) If each wire must be 20 m long, what diameter of wire should be used?

b) If the current in the wire is 4.0 A, what is the potential drop across the wire?

Temperature and Resistivity

• Resistance is also dependent on temperature.

• At higher temperatures, the atoms are moving more rapidly and in a less orderly fashion.

• This results in a greater interference with the current.

Temperature and Resistivity

• Therefore, resistivity increases as temperature increases in most materials.

• The main exception to this rule is semiconductors.

Problems

• Do problems 12, 13, 14, and 16 on page 516.

• We will whiteboard these problems at the end of class.

Whiteboarding Groups

Group Members Problem

1 Drew, Abbey, Aidan 5

2 Sarah, John, Angi 7

3 Rachel, Ellen, Connor 9

4 Miggy, Bailey, Armen 12

5 Anthony, Brie, Robert 13

6 Krystiana, Jacob 14

7 Piper, Jeremiah, Kaleb 16

Homeowork

• Do problem 21 on page 516.

• This is the only problem I am assigning tonight. I expect you to put a full 30 minutes of effort into this problem.

Power

Power

• In physics, power is defined as the rate at which work is done.

• An alternative definition is the rate at which energy is transferred.

Power

• If power is not being delivered at a constant rate, we need calculus to find it.

• However, we can define average power.

• In DC circuits, power is delivered a constant rate, so average power is also the power at any instant.

Power

• In an electric circuit, we have charges moving through a potential difference across a wire.

• We learned in Unit 2 that these charges have potential energy given by

Power

• Since the charge is continually moving, it makes more sense to talk about power rather than energy.

• We often want to know how much energy is being delivered to a device in a circuit by the moving charges.

Power

• Recall the definition of power:

• For one charge, the energy delivered is QV. However, we have many charges flowing, so the energy is

Power

• So, the power delivered in a time t is

• But notice that Q/t is the current through the wire (I). So, the power delivered by the circuit is

Power

• We can also combine this formula with Ohm’s Law.

• With this, we can get two other expressions for power

A Quick Warning

• These alternate equations are only true for the power delivered to a resistor.

• However, P=IV is true for any part of the circuit.

Power

• The unit of power is a J/s.

• This is known as a watt (W).

• However, you usually pay for electricity in terms of energy. This is power times time.

• Energy companies usually measure energy in kilowatt-hours (kWh).

ExampleA typical headlight bulb in a car draws 40 W of power. If the light draws its power directly from a 12 V car battery,

a) Calculate the current flowing through the bulb.

b) Calculate the resistance of the bulb.

Example

An electric heater draws a current of 15 A from a standard 120 V wall socket.

a) How much power is delivered to the heater?

b) If the heater is operated 3 hours a day for a 30 day month, how much does it cost to operate the heater? Assume electricity costs 9.2 ¢/kWh.

Homework

• Read 18-5.

• Do problems 27-33 odd on pages 516-517.

Homework

• Do problems 26-32 even on pages 516-517.

Household Electricity

Lightbulbs, Fuses, and Circuit Breakers

Lightbulbs

• A lightbulb is a device that converts electrical energy into light (and heat).

• There are two types of lightbulbs.– Incandescent– Fluorescent

Incandescent Bulbs

• In an incandescent bulb a current is passed through a filament encased in an evacuated glass bulb.

• The filament quickly becomes hot and begins to glow.

Incandescent Bulbs

• Since the filament is glowing, it gives off light.

• It also gives off a great deal of heat.

• In order to make the filament glow sufficiently brightly, a fair amount of power is needed.

Fluorescent Bulbs

• Fluorescent bulbs operate on a different principle than an incandescent.

• A fluorescent bulb is filled with a gas (usually Argon).

• When the bulb is connected to a battery, some of the gas molecules become ionized.

Fluorescent Bulbs

• Current is able to flow throughout the tube.

• As electrons flow, the sometimes strike other gas molecules.

• This collision excites at least one electron in the molecule to a higher energy level.

Fluorescent Bulbs

• As the excited electron returns to its original energy level, it releases its excess energy as a photon.

• The color of the light depends on the how much the electron was excited.

• Fluorescent bulbs have a coating to control the color of light emitted.

Fuses and Circuit Breakers

Fuses

• Although wires generally have very low resistance, their resistance does cause some electrical energy to be lost as heat.

• The rate of heating is equal to the power delivered through the wire.

Fuses

• If the current is very large, the wire can heat up to the point of becoming a fire hazard.

• A fuse is a piece of metal placed in the circuit.

Fuses

• The metal in the fuse melts when the temperature in the circuit gets too high.

• When the fuse melts, the circuit is broken, thereby preventing a fire.

Circuit Breakers

• A circuit breaker operates on a similar principle.

• When the temperature gets too hot, the bimetallic strip bends and the circuit is broken.

Circuit Breakers

• Circuit breakers are generally preferable because they can be reset without being replaced.

• When a fuse has been blown, it must be replaced with a new fuse in order for the circuit to function.

Homework

• Read 18-6.

• Do problems 35, 37, and 39 on page 517. Check your answers with the back of the book.