Physics 3204: Current Electricity Notes - Carbonear …...Physics 3204: Current Electricity Notes 1 Factors Affecting Current •the natural state of electrons in a wire, or other

Physics 3204: Current Electricity Notes

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Factors Affecting Current

• the natural state of electrons in a wire, or other conductor, is to simply spread out

• a battery, or other power supply, will given electrons energy to move through a complete circuit

• the physics convention is that electrons will flow through a circuit from the direction of the negative terminal of a battery back through to the positive

• engineers use the opposite convention (positive flow)

• current is measured by an ammeter, galvanometer, or multimeter placed in series

A

A

correct incorrect

battery

resistor

ammeter

• current is affected by several key factors

> resistance of the material> temperature> crosssectional area> energy / voltage> number of pathways

https://www.youtube.com/watch?v=1xpjes-shwg


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Circuit Diagrams

Key symbols

Resistor:

Power Supply:

Switch:

Fuse:

A6V

3Ω

AAmmeter:

Voltmeter: V

V

4.5 A

3.8Ω

A

Ex) What does the ammeter read?

Ex 2) What does the voltmeter read?


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Kirchoff's Laws

Current Law: current into a junction is equal to the current that comes out of the junction

• current in series is constant (no junction)• current in parallel separates (total current constant)

Ex 1) An ammeter in series with a resistor reads 5 A. What is the current through the resistor?

Ex 2) There is 10 A of current into a parallel junction. If 3 A of current enters the first path, what is the current in the second path?

Ex 3) In the previous example, why might the current be different in each path?

.


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Voltage Law: the total potential decrease (voltage drop) is equal to the total potential gain (voltage gain) in a given loop

• in series, the voltage used will total the voltage available• in parallel, the total voltage in each branch will be equal (not spilt)

6V 2 V

Ex 1) What is the potential difference across the second resistor?

6V

Ex 2) What is the potential difference across each resistor?


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Resistance

• total resistance, or equivalent resistance depending on the situation is different in series and parallel

• in series, resistance is additive (much like drive thru, each item of resistance makes the total resistance greater)

• in parallel, resistance has an inverse relationship (must like grocery store lineups, the more open lanes the faster everyone moves regardless of the speed of any given line)

Series: RT = R1 + R2 + R3 + .....

Parallel: 1/RT = 1/R1 + 1/R2 + 1/R3 + .....

Ex) A 5 Ω, 3 Ω, and 6 Ω resistor are put together. What is the total resistance if:

a) the are all in series

b) the are all in parallel

c) they are arranged as shown5 Ω 3 Ω

6 Ω


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Putting It Togetherlearn to organize yourself, possibly with a table

1) Given the following circuit.

a) What is the total current

b) What is the voltage across the 2 Ω resistor?

6V 5 Ω

2 Ω

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2) Given the following circuit.

a) What is the total current?

b) What is the total resistance?

c) What is the voltage drop across the 4 Ω resistor?

4 A2 A2 Ω

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Extra Practice16 V4.0 A

1) 3 Ω

2)

2.5 Ω

2.5 Ω

5.0 Ω

12 V

5 Ω

4 Ω

6 V

2.0 A fuse

3)

Calculate the missing values

Calculate the missing values

Will the fuse blow?


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4 Ω

2 Ω9 V

4 Ω

Ex 2)

1) Total resistance Find the following

2) Current through the 2 ohm resistor.

3) Voltage drop across the resistor in series with the battery.


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(i) What is the total resistance?

(ii) What is the current through each resistor?

Cheat Sheet

(i) What is the total resistance?• Find equilivalent resistance of 2 and 3• Use series rule for resistance to find total resistance

(ii) What is the current through each resistor?• Find total current using ohm's law (V = I R)• Use series rule to determine current through 1 and 4• Find voltage drop across 1 and 4• Use voltage rule for parallel to determine voltage in 2 and 3• Find current through 2 and 3 using ohm's law


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Combination Circuits

• many circuits have some parts that are in series and others that are in parallel

• in order to deal with these, we often create equivalent resistances for the different sections

4 Ω

2 Ω

6 V

3 Ω

Ex)

1) What is the total resistance?

2) What is the potential difference across the 4 Ω resistor?

3) What is the current through the 3 Ω resistor?


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(i) What is the total resistance?(ii) What is the voltage across resistor 2?(iii) Will the fuse blow?

Cheat Sheet

(i) What is the total resistance?• Find equilivalent resistance of 2 and 3• Use series rule for resistance to find total resistance (fuse provides no resistance)(ii) What is the voltage across resistor 2?• Find total current using ohm's law• Use series rule to determine current through 1• Use ohm's law to determine voltage across 1• Use parallel rule to determine voltage across 2(iii) Will the fuse blow?• Fuses blow when max current is reached• Since the fuse is in series with 3, find current through 3 using ohm's law


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Resistance

• a measure of how current is restricted through an object• measured in ohms• resistance depends on:

1) resistivity of the material (ρ "rho")• constant for a given material• for example, all copper wires have the same resistivity (1.7 x 108 Ω m) but many have a different resistance

2) crosssectional area (A)• A = πr2 for a circular wire• larger area allows more room for current to flow

3) length (L)• greater length causes more obstacles over the whole path impeding current

4) Temperature (not in equation)• increased temperature causes electrons to move quicker causing more collisions

• this leads to an overall increase in resistance

R = ρ L / A


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Ex) Tungsten has a resistivity of 5.6 x 108 Ω m. What is the resistance of a 1.2 m long tungsten wire with a radius of 1.0 x 103 m?

Ex 2) A pencil has a length of 0.17 m and the "lead" has an area of 1.5 x 102 m. Graphite has ρ = 3.6 x 105 Ω m. What is the resistance of the pencil?


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• typically, the resistance is calculated based on changing factors

Ex 3) A 200 m piece of wire has a resistance of 1.7 Ω. What is the resistance of a 50 m piece cut from it?

Ex 4) A piece of copper has a resistance of 5.0 Ω. If it is compressed so that the length is halved and the area is tripled, what is the new resistance?


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Sources of Electrical Energy

Voltaic Cells

Piezoelectric Energy

Thermoelectric

Photoelectric Energy

Generators

Energy

https://www.youtube.com/watch?v=zqp0q4b4t44

https://www.youtube.com/watch?v=rzb3vfi3sew

https://www.youtube.com/watch?v=gveiqsgvfum&list=uuluvpd1qo0e6fmzulebnx6w

https://www.youtube.com/watch?v=x2zjdtxrisc

https://phet.colorado.edu/en/simulation/generator

https://www.youtube.com/watch?v=yhynskfljos


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Power

• recall that > P = W x t > V = W / q> I = q / t

• from this we can see the equation for electrical power

• using Ohm's law, we can also determine two additional power equations

Using I = V / RUsing V = I R

• while power can be a standalone question, it is typically added on to circuit diagram questions


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1) A 120 V source is used to power a 1.0 A charger. How much power is dissipated in the charger?

2) A 11 W bulb is connected to a 120 V source. What current flows through the bulb?

3) A 8.0 Ω resistor is connected to a 1.5 V battery. What is the power dissipated by the resistor?

4) A 3.0 Ω and a 5.0 Ω resistor are connected in parallel with a 12 V battery. What is the power generated by the battery?

.


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Cost of Electricity


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• the power company charges for electricity based on the kilowatt hour (a convenient unit for energy)• to determine the number of kWh used, we simply multiply the power (in kW) by the time used (in hours)• this can then be multiplied by the current electricity rate (currently 11.178¢ per kWh)• in simplest form

cost = P t rwhere P is power in kW

t is time in hoursr is rate in either ¢ per kWh or $ per kWh

Ex) One 60 W incandescent lightbulb is replaced with an 8 W LED light. If the bulbs were both operated for 5 hours a day, how much was saved?

Ex 2) In a particular home there are 25 13 W CFL bulbs. If the average time used per day is 6 hours, how much would it cost to operate them over a month?

.


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Energy Use in Canada

• keep in mind that the energy use in most examples will be quite low compared to what you might expect

• this is because most of the energy in a typical home goes toward the heating of air and / or water

• these costs tend to be harder to estimate as it is harder to determine the exact run time of heaters and the wattages can be difficult to obtain

http://www.cornhusker-power.com/householdappliances.asp


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Physics 3204: Current Electricity Notes - Carbonear …...Physics 3204: Current Electricity Notes 1 Factors Affecting Current •the natural state of electrons in a wire, or other