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1. In the electric circuit shown, there is a

a) transfer of energy from

b) transformation of energy from

Electric Circuits

a) closed pathway for transfer of energy: b) flow of electrons that transfer the energy: c) source of electrical potential energy: examples: d) device that uses the energy: examples:

2. In general, an electric circuit contains a:

Cell:

Dry cell:

Wet cell:

Primary cell:

Secondary cell:

Battery:

3. What does it mean for a battery to be rated at 1.5 V?

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Electric current:

Formula:

4. How much is 1 ampere (1 amp) of current?

Units:

5. What is the current in a wire in which 600. C of charge pass a point every 4.0 minutes?

6. If a 12.0 A current is allowed to flow for 20. seconds in a circuit, how many elementary charges pass that point?

Direct Current (DC):

Electron flow: Conventional current:

Source of DC:

Official Definition of One Ampere (1 A) One ampere is the amount of current flowing in each of two infinitely-long parallel wires of negligible cross-sectional area separated by a distance of one meter in a vacuum that results in a force of exactly 2 x 10-7 N per meter of length of each wire. Short form – Current is defined in terms of the force per unit length between parallel current-

carrying conductors.

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Alternating Current (AC):

Source of AC:

a) positive lattice ions fixed in place b) freely moving conduction electrons that carry charge

Model for the structure of a metal conductor (like a wire or filament)

Without an applied potential difference . . .

drift speed:

7. Compare the instantaneous speed of the conduction electrons with their drift speed.

Instantaneous speed – Drift speed –

When a potential difference is applied across the conductor . . .

a) an electric field is set up in the conductor,

a) conduction electrons accelerate to the positive terminal

b) and collide with lattice ions thus transferring

energy to them.

Drift Speed formula

n = charge density = number of charge carriers per unit volume (per 1 m3 of volume)

A = cross-sectional area q = charge v = drift speed

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Derivation

In the figure above, charge carriers, each with chare q, move past point P with a speed v.

a) In one second, the volume of charge carriers passing P is equal to

b) The total number of charge carriers in this volume is

c) The total charge of the charge carriers in this volume is

d) Therefore, the current is

8. A copper wire of diameter 0.65 mm carries a current of 0.25 A. There are 8.5 x 1028 charge carriers in each cubic meter of copper. Calculate the drift speed of the charge carriers.

9. If the drift velocity is so small, why does the light bulb light as soon as the battery is connected?

Conduction electrons already in the filament start to move as soon as the electric field is set up in the circuit by the battery. It is these electrons, not the electrons from the battery, that collide with the lattice ions in the filament immediately and transfer enough energy to them to make the filament glow.

1. What is the cause of resistance in a wire?

Resistance of a Wire

Factor Symbol Unit Less Resistance

More Resistance Relationship

Length

Cross-sectional

Area

Resistivity

Temperature

Symbol: Unit:

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Formula for a conducting wire at a constant temperature . . .

3. What are the properties of wire that is the worst conductor (has the most resistance)?

2. What are the properties of wire that is the best conductor (has the least resistance)?

4. What material would you use to make a wire with the:

b) most resistance a) least resistance

6. a) What is the resistance of a nichrome wire 12 meters long with a diameter of 2.7 × 10-4 meter?

5. What is the resistance of a copper wire 2.0 meters long with a cross-sectional area of 6.4 × 10-8 m2?

b) If the diameter of the wire above is doubled, what is its resistance?

Simple Circuits

Schematic:

Schematic Diagram of

Circuit

Draw a corresponding schematic diagram using appropriate Circuit Symbols.

Actual Circuit

Schematic Diagram of

Circuit Actual Circuit

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1. For the electric circuit shown at right, what is the potential at:

Point A Point B Point C Point D

2. For the electric circuit shown, what is the potential difference from:

A→B B→C C→D D→A

Electrical resistance: Formula:

Water Analogy for a simple circuit

Electromotive force (emf): conversion from some other form of energy into electrical energy

Potential difference (pd): conversion from electrical energy into some other form of energy

Variable V I R

Quantity

Units

Type

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3. What is the resistance of a small appliance that draws 3.00 A at 120 Volts?

Ohm’s Law: This means that

I. Ohmic device:

Slope: II. Non-ohmic device:

4. Why is a filament lamp non-ohmic?

Slope:

Example:

Example:

Relationship:

I-V characteristics for various non-ohmic conductors

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Open circuit:

Short circuit:

Closed circuit:

6. Determine the readings on the meters when the switch is open and when it is closed.

Meter Reading

when Open

Reading when

Closed

Ammeter: Types of Meters

Voltmeter:

5. Draw a circuit diagram to include a 6.0 V battery hooked to a 12.5 Ω resistor. Include an ammeter reading the current in the circuit and a voltmeter to measure the potential difference across the resistor. Determine the reading on each meter.

Placement: Must be placed to allow current to flow through it Circuit must be broken to insert ammeter. Ideal ammeter: has internal resistance so it will not affect current flowing through it

Placement: Must be placed to measure potential difference between two points Placed outside circuit – no need to break circuit

Ideal voltmeter: has internal resistance so it will not allow any current to flow through it rather than the circuit

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9. If the resistor is set to 100 ohms, what is the current in the circuit?

7. What are some common uses for a variable resistor?

Variable Resistor:

8. If the resistance in the circuit is increased, what will happen to the brightness of the lamp? Why?

Electrical Power and Energy

Power:

Electrical Mechanical Power

Electrical Energy

Units:

1. A mini light bulb is connected to a 1.5 volt battery and draws a current of 28 mA.

b) How much energy does the light bulb use in 1.0 minute?

a) How much power does it dissipate?

Also called:

Units: Units:

Electrical Power

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Slope:

2. Refer to the drawing of a motor lifting a brick.

b) How much energy will the motor use in 10.0 seconds?

a) How fast can the motor raise a 2.0 kg brick?

4. If the resistance of an appliance attached to a constant source of voltage is doubled, how much power does it now dissipate?

5. The electric meter connected to a house is marked “kilowatthours.” The electric bill lists a charge to the homeowner for using 471 KWH (kWh) for the month. What is being measured in kilowatthours?

7. Determine the energy cost for the consumer whose bill is shown above.

3. Sketch each of the following relationships:

Kilowatt-hour (kWhr): 6. How many joules of energy are equivalent to one kilowatt-hour?

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8. a) How much energy is used lighting a 60. W bulb for 4.5 hours? Answer in joules and kilowatt-hours.

9. A DC power charger is marked as “5.0 V 3.5 VA.”

a) What quantity is being measured as 3.5 VA?

b) How much current does the charger use?

10. A resistor is marked as 270 Ω with a power rating of 0.50 W.

a) What is the maximum current this resistor can safely handle?

b) What will happen if there is more current than this maximum amount in the resistor?

11. A cell-phone battery is marked as “90 mA h 12 V 1.08 Wh”.

a) What quantity is being measured as 90 mAh?

b) Determine how much energy is stored in the battery.

Capacity:

at 90 mA for ______ hour or at 45 mA for ______ hours or at 9 mA for ______ hours, etc.

A battery whose capacity is 90 mA h means that before it “dies” and needs recharging you can run it:

12. A cell has a capacity of 1400 mA h. Calculate the number of hours for which it can supply 1.8 mA.

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Series and Parallel Circuits

Combining Light Bulbs in Series

1. Build a circuit with one light bulb and observe its brightness. The brightness of a bulb is a measure of . .

PREDICTION RESULT

Power of an individual bulb

Total power of the circuit

Resistance of an individual bulb

Total resistance of the circuit

Total potential difference across the circuit

Potential difference across an individual bulb

Total current in the circuit

Current through an individual bulb

3. Unscrew one light bulb from its base (but leave the base in the circuit). What happens to the other light bulb? Why?

R

V

I

P

3 V

Bulb #1

Bulb #2

Circuit Total

R

V

I

P

3 V

4. Assume each light bulb has a constant resistance of 10 Ω. Analyze each circuit.

2. Add a second bulb in series. Observe or infer what happens to the:

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Analyzing Series Circuits

1. Current: Current is the same at all points in a series circuit. Current is the same through each resistor.

2. Voltage: The increase in potential provided by the battery is equal to the sum of the potential drops across each resistor.

NOTE:

NOTE:

Kirchhoff’s Second Law (Voltage Law, Loop Rule):

3. Resistance: The total resistance of the circuit is the sum of the individual resistances.

Equivalent resistance –

4. Power: The total power used in the circuit is the sum of the power used by the individual resistors.

NOTE: .

NOTE:

Series relationships 5. In a series circuit, which resistor, if any, will . . . a) have the greatest potential difference across it? b) have the most current running through it? c) dissipate the most power? d) shine brightest (if it is a light bulb)?

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6. Determine the current through each resistor, the potential drop across each resistor, and the power dissipated by each resistor in the circuit below.

7. Find the potential difference across each resistor, the current through each resistor, and the power used by each resistor.

1. The graph below shows the I-V characteristics of two conductors, X and Y. The conductors are connected in series to a battery whose voltage is such that the power dissipated in each of the two resistors is the same.

a) Determine the resistance of each resistor.

b) Determine the total voltage of the battery.

c) Determine the total power dissipated in the circuit.

d) The battery is replaced by another one such that the current through X is 0.2 amps. Determine the voltage of this battery.

I-V Characteristics

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Combining Light Bulbs in Parallel

1. Build a circuit with one light bulb and observe its brightness

PREDICTION RESULT

Power of an individual bulb

Total power of the circuit

Resistance of an individual bulb

Total resistance of the circuit

Total potential difference across the circuit

Potential difference across an individual bulb

Total current in the circuit

Current through an individual bulb

3. Unscrew one light bulb from its base (but leave the base in the circuit). What happens to the other light bulb? Why?

R

V

I

P

3 V

Bulb #1

Bulb #2

Circuit Total

R

V

I

P

4. Assume each light bulb has a constant resistance of 10 Ω. Analyze each circuit.

2. Add a second bulb in parallel. Observe or infer what happens to the:

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Analyzing Parallel Circuits

2. Current: The total current coming out of (and going back into) the battery is equal to the sum of the individual currents going through each resistor.

1. Voltage: The increase in potential provided by the battery is equal to the potential drop across each resistor.

4. Resistance: The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.

3. Power: The total power used in the circuit is the sum of the power used by the individual resistors. NOTE:

NOTE:

5. A 3.0 Ω and a 6.0 Ω resistor are connected in parallel. What is their equivalent resistance?

Parallel relationships 6. In a parallel circuit, which resistor, if any, will . . . a) have the greatest potential difference across it? b) have the most current running through it? c) dissipate the most power? d) shine brightest (if it is a light bulb)?

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Shortcut for identical parallel resistors:

7. Calculate the equivalent resistance of each resistor segment below.

8. Calculate the voltage drop across each resistor and the current through each resistor. Calculate the total current in the circuit and the equivalent resistance of the circuit.

9. A 50. Ω, a 100. Ω and a 150. Ω resistor are to be connected in the circuit below between A and B. What type of connection will have the highest resistance? The lowest resistance? Complete each circuit and calculate each current.

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13. A 12 Ω heater, a 20 Ω hair dryer, and a 25 Ω toaster are connected in parallel to a 120. volt power source. Sketch an appropriate schematic. Include a meter capable of measuring the total current and a meter capable of measuring the voltage drop across the heater. Find the reading on each meter.

11. Determine the current through each resistor by using a proportion.

12. Determine the current through each resistor in the circuits below using a proportion.

10. Calculate the voltage drop across each resistor and the current through each resistor. Calculate the total current in the circuit and the equivalent resistance of the circuit.

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Kirchhoff’s First Law (Current Law, Junction Rule):

NOTE:

Junction:

Junctions

1. Determine the magnitude and direction of the current in the unlabeled wire.

Junction A Junction B Junction C

2. Determine the reading on each blank ammeter. 3. Determine the new readings now that the 9 Ω resistor is removed.

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Review - Resistors in Series or in Parallel

Parallel Connection

Characteristic Series Circuit Parallel Circuit

Number of pathways for current

Current

Potential Difference (Voltage)

Overall resistance

Power

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Household Wiring

2. Draw an appropriate schematic for the household circuit shown.

1. Is most household wiring in series or in parallel? Explain.

4. A 900 watt toaster, a 640 watt waffle iron, and a 5 amp food processor are to be used on the same circuit. What size circuit breaker should be used?

3. What is the purpose of a fuse or a circuit breaker? How are they different?

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Combination Circuits

In each circuit below, determine the voltage drop across each resistor and the current through each resistor.

2.

1.

3.