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4.2.1 Electrical Current
Definitions
• current – ________________________________________ • unit: _____________ or _______________
• requires:
– _______________________________________ – _______________________________________
Equation
Example #1
• 100 coulombs of charge pass through point A in 4.0 seconds. – What is the rate of current flow through point A?
Example #2
• During a thunderstorm a lightning strike transfers 15.0 coulombs of charge in 10.0 milliseconds.
– What was the electrical current produced in the strike?
• A wire carries a current of 50 amperes.
– How much charge flows through the wire in 10 seconds?
– How many electrons pass through the wire in 10 seconds?
PRACTICE
1) A wire allows 2.5 x 1015 electrons to flow through it every 8.0 seconds. What is the current passing through the wire in amperes?
4.2.2 Electrical Resistance
Definitions
• resistance – ________________________________________ • unit: _____________
• factors that change resistance
– resistivity: ______________________ – length
– cross-sectional area – temperature
Equation
Resistance Factors
• To build an “ideal” conductor with the smallest possible resistance you would select one that is: ___________________________________________________________ Review Questions
4.2.1 – Use electrical current equation to determine current, charge, or time. Determine number of electrons flowing based on current or current based on number of electrons.
- What is the amount of electrical current passing through a wire if 35 coulombs of charge flow through it in 5.0 seconds?
[7A]
- If a 2.5 ampere current is flowing through a given point on a wire, how long would it take for 100 coulombs of charge to pass this point?
[40s]
- How much charge passes through a wire if a current of 10 ampere flows through it for 30 seconds?
[300C]
- How many electrons per second are flowing through a point in a wire that has 5.0 amperes of current passing through it?
[3.125E19]
- 6.4 x 1014 electrons pass through a given point every second. What amount of electrical current does this represent?
[4A]
R
ρ
R
A
R
L
R
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Example #1
• Determine the resistance of a 1.0 meter long copper wire with a cross-sectional area of 0.01 meter2.
Example #2
• A piece of wire that has a length of 5.0 x 107 meters and a cross-sectional area of 0.025 meter2 has a resistance of 31.8 ohms.
– What is the composition of this wire?
PRACTICE 1) A 100 meter long wire has a resistance of 10 ohms.
a. If it is cut into four equal length pieces, what is the resistance of each piece?
b. If its cross-sectional area were doubled without changing its original length, what would its new resistance be?
Review Questions
4.2.2 – Use equation to determine resistance, resistivity, length and/or cross-sectional area. Determine composition of a wire. Explain the relationship between resistance and various factors that impact resistance.
- What is the resistance of a copper wire with a cross-sectional area of 2.0 x 10-6 meter2 and a length of 50 meters?
[0.43Ω]
- What is the length of an aluminum wire with a resistance of 25 milliohms if it has a cross-sectional area of 4.0 x 10-4 meter2?
[355m]
- What is the composition of a wire with a resistance of 8.13 ohms if its cross-sectional area is 3 x 10-6 meter2 and its length is 1000 meters?
[gold]
- Compared to wire A which has a resistance of 10 ohms, wire B has twice the length and half the cross-sectional area. What is the resistance of wire B?
4.2.3A Ohm’s Law
Ohm’s Law - Factors
• Voltage results in current flow
– More voltage = ______________________________
• Resistance opposes current flow
– More resistance = _____________________________ Equation
Example #1
• A potential difference of 25.0 volts is supplied to a circuit with 100 ohms of resistance. – How much current flows through the circuit?
Example #2
• A current of 2.0 amperes flows through a 10 ohm resistance.
– What voltage must be supplied to this resistance?
Example #3
• A 10 volt battery establishes a current of 5.0 amperes in a circuit.
– What is the resistance of this circuit?
Circuit Elements
Proper Use of Meters _________________
measures: _______________ resistance: _______________
connect to circuit: ____________
_________________ measures: _______________ resistance: _______________
connect to circuit: ____________
5 V 2.5 Ω
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4.2.3B Electrical Power
Power Law
• Moving electrons (current) requires ENERGY
– How much energy gets used depends on:
• Strength of push - __________________________
• Rate of flow - ______________________________ Equations
Example #1
• A 12 volt battery is connected to a circuit which allows 10 amperes of current to flow. – What is the power of this circuit?
Example #2
• A 100 watt light bulb is connected to a 120 volt power supply.
– What amount of current must pass through the light bulb?
Example #3
• A 2.0 ampere current passes through a circuit with a 300 ohm resistance.
– What is the power generated in this circuit?
PRACTICE
1) A 200 watt heater is run for 5.0 seconds using a 110 volt potential difference. a. Calculate the amount of heat ENERGY produced by the heater in this time.
b. Calculate the current passing through the heater.
2) What is the power dissipated by a 550 ohm resistor that is connected to a 10.0 volt source of electrical potential.
3) A toaster with an internal resistance of 11.0 ohms is connected to a 110 volt source of electrical potential (standard outlet).
a. Calculate the power used by the toaster.
b. How much energy is used by the toaster if it takes one minute to produce a slice of toast?
c. Energy usage in the home is calculated in kilowatt-hours rather than joules. If 1 joule = 2.78 x 10-7 kW·h, what is the energy from (b) in kW·h?
d. If the typical cost for electrical energy in New York State is ¢14 per kW·h, how much does it cost to make a slice of toast?
e. How many slices of toast can you make for a penny?
Review Questions
4.2.3 – Use Ohm’s Law and Power Law to perform calculations. Analyze graphs to relate voltage, current, resistance, and/or power. Recognize and sketch simple circuits with switches, batteries, meters, and/or resistances.
- How much current will pass through a 30 ohm resistor when it is connected to a 90 volt source of electrical potential?
[3A]
- What is the resistance of a heater that allows 12 amperes of current to flow through it when it is connected to a 120 volt source?
[10Ω]
- How much power is generated by a light bulb that draws 0.2 ampere of current when connected to a 6.0 volt battery?
[1.2W]
- How much current is drawn by a 4400 watt motor if it is operated at an electrical potential of 220 volts?
[20A]
- What is the resistance of a component that generates 300 watts of power while allowing 0.5 ampere of current to pass through it?
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4.2.4 Series Circuits
Definition and Rules
• series circuit – a circuit in which two or more elements are connected end-to-end so that a single loop of current is formed
• equivalent resistance – more resistors = more resistance
– ____________________________________________________ • current – same current throughout
– ____________________________________________________ • voltage – voltages add up
– ____________________________________________________ • All circuit components and the circuit as a whole must obey Ohm’s Law.
Example #1 - Sketch a graph of current vs. voltage for a fixed resistance.
o What does the slope of this graph represent?
o Sketch a graph of current vs. voltage for an object that does NOT obey Ohm’s Law.
[direct; slope-=R any non-linear graph]
- In which cases are the meters connected incorrectly?
[B, C]
V I
V I
Fixed Resistance Non-fixed Resistance
A
V
A
V (A)
(B)
(C)
(D)
V (V) I (A) R (Ω)
R1 5.0
R2 8.0
R3 2.0
Example #2
PRACTICE
1. The battery in the circuit below supplies it with a potential difference of 160 volts. a. Determine all unknown quantities in this circuit.
b. Add an ammeter to the circuit so that it reads the current passing through resistor R2.
c. Add a voltmeter to the circuit so that it reads 100 volts.
2. Draw a series circuit that contains: a 1.0 ohm resistor, a 3.0 ohm resistor, a 12 volt battery, a switch, an ammeter, and a voltmeter that will measure the potential difference of the battery.
3. Complete the circuit chart below, then sketch the circuit that it describes.
V (V) I (A) R (Ω) R1
R2 R3 Req
R1
10 Ω
R2
20 Ω
R3
50 Ω V (V) I (A) R (Ω)
R1 50
R2 120
R3 150
Req 1.5
V (V) I (A) R (Ω) R1 280
R2 10
R3 60
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4.2.5 Parallel Circuits
Definition and Rules
• series circuit – a circuit in which two or more elements are connected so that each has its own current loop.
• equivalent resistance – more resistors = less resistance
– ____________________________________________________ • current – currents add up
– ____________________________________________________ • voltage – voltages same for each resistor
– ____________________________________________________ • All circuit components and the circuit as a whole must obey Ohm’s Law.
Junction Rule
• The total current flowing into and out of a junction must be the same.
Example #1
Example #2
V (V) I (A) R (Ω)
R1 20
R2 50
R3 0.5 10
Req
V (V) I (A) R (Ω)
R1 30
R2 30
R3 30
Req 60
10A
4.0A
10A
2.0A
6.0A
PRACTICE
1. The battery in the circuit below supplies it with a potential difference of 160 volts. a. Determine all unknown quantities in this circuit.
b. Add an ammeter to the circuit so that it reads the current passing through resistor R1.
c. Add a voltmeter to the circuit so that it reads the battery voltage.
2. Use the Junction Rule to determine current “X” in each diagram.
3. Sketch a parallel circuit that has a 20 ohm resistor, a 40 ohm resistor, a battery that provides 10 volts of electrical potential, and an ammeter that reads the current passing through the 20 ohm resistor.
Review Questions
4.2.4/5 –Explain the difference between series and parallel circuits. Explain how the Junction Rule works and use it to determine unknown currents. Solve circuits of either type using charts, Ohm’s Law, and Power Law. Determine the effect of adding/removing resistors and opening/closing switches on circuits. Compare equivalent resistances of different circuits and/or arrangements of resistors.
- A 30 ohm resistor and a 20 ohm resistor are connected in series with a 100 volt battery. The electrical current that would pass through the 20 ohm resistor is
(1) 5 A (2) 2 A (3) 7 A
- A 30 ohm resistor and a 20 ohm resistor are connected in parallel with a 100 volt battery. The electrical current that would pass through the 20 ohm resistor is
(1) 5 A (2) 2 A (3) 7 A
[2;1]
- A 30 ohm resistor and a 20 ohm resistor are connected in series with a 100 volt battery. The electrical potential that is measured across the 30 ohm resistor in this circuit would be:
(1) < 100 V (2) 100 V (3) > 100 V
- A 30 ohm resistor and a 20 ohm resistor are connected in parallel with a 100 volt battery. The electrical potential that is measured across the 30 ohm resistor in this circuit would be:
(1) < 100 V (2) 100 V (3) > 100 V
[1;2]
V (V) I (A) R (Ω) R1
R2 R3 Req
5 A
2 A
X
8 A
5 A X
X 7 A 4 A 10 A
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- Determine the unknown current and its direction in each diagram.
[2A; 4A; 2A]
- Determine the equivalent resistance of… a. three 90 ohm resistors in series b. three 90 ohm resistors in parallel
c. a 10 ohm resistor and 20 ohm resistor in series d. a 10 ohm resistor and 20 ohm resistor in parallel e. 5, 10, and 40 ohm resistors in series
f. 20, 30, and 40 ohm resistors in parallel g. 120, 142, and 312 ohm resistors in series h. 311, 416, and 520 ohm resistors in parallel
[270Ω; 30Ω; 30Ω; 6.7Ω; 55Ω; 9.2Ω; 574Ω; 132Ω]
- Which has the least resistance?
(1) four 8 ohm resistors connected in parallel (2) two 8 ohm resistors connected in series (3) a single 8 ohm resistor
(4) a pair of 2 ohm resistors connected in series
[1]
- Two 20 ohm resistors are connected in parallel. If a third 20 ohm resisstor is connected to them in parallel the equivalent resistance of the circuit will
(1) increase (2) decrease (3) not change
- Two 20 ohm resistors are connected in seriesl. If a third 20 ohm resisstor is connected to them in series the equivalent resistance of the circuit will
(2) increase (2) decrease (3) not change
[2; 1]
3A 7A ?
3A ?
5A 5A
7A
? 6A
