Download Physics 3204: Current Electricity Notes

Physics 3204: Current Electricity Notes
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 battery
resistor
A
A
ammeter
correct
incorrect
• current is affected by several key factors
>
>
>
>
>
resistance of the material
temperature
cross­sectional area
energy / voltage
number of pathways
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Physics 3204: Current Electricity Notes
Circuit Diagrams
Key symbols
Resistor:
Ammeter:
A
Power Supply:
Voltmeter:
V
Switch:
Fuse:
Ex) What does the ammeter read?
6V
A
3Ω
Ex 2) What does the voltmeter read?
4.5 A
A
3.8Ω
V
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Physics 3204: Current Electricity Notes
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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Physics 3204: Current Electricity Notes
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)
Ex 1) What is the potential difference across the second resistor?
6V
2 V
Ex 2) What is the potential difference across each resistor?
6V
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Physics 3204: Current Electricity Notes
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 shown
3 Ω
5 Ω
6 Ω
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Physics 3204: Current Electricity Notes
Putting It Together
learn 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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Physics 3204: Current Electricity Notes
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?
2 A
2 Ω 4 A
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Physics 3204: Current Electricity Notes
Extra Practice
16 V
4.0 A
3 Ω
1) Calculate the missing values
2.5 Ω
12 V
2) 2.5 Ω
5.0 Ω
Calculate the missing values
3) 6 V
5 Ω
4 Ω
2.0 A fuse
Will the fuse blow?
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Physics 3204: Current Electricity Notes
2 Ω
Ex 2)
9 V
4 Ω
4 Ω
Find the following
1) Total resistance 2) Current through the 2 ohm resistor.
3) Voltage drop across the resistor in series with the battery.
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Physics 3204: Current Electricity Notes
(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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Physics 3204: Current Electricity Notes
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
Ex)
4 Ω
6 V
3 Ω
2 Ω
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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Physics 3204: Current Electricity Notes
(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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Physics 3204: Current Electricity Notes
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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Physics 3204: Current Electricity Notes
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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Physics 3204: Current Electricity Notes
• 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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Physics 3204: Current Electricity Notes
Sources of Electrical Energy
Voltaic Cells
Piezoelectric Energy
Thermoelectric Energy
Photoelectric Energy
Generators
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Physics 3204: Current Electricity Notes
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 V = I R
Using I = V / R
• while power can be a standalone question, it is typically added on to circuit diagram questions
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Physics 3204: Current Electricity Notes
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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Physics 3204: Current Electricity Notes
Cost of Electricity
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Physics 3204: Current Electricity Notes
• 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 r
where P is power in kW
t is time in hours
r 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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Physics 3204: Current Electricity Notes
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
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