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Current

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Current Current is defined as the flow of positive charge. Current is defined as the flow of positive charge. I = Q/t I = Q/t I: current in Amperes or Amps (A) I: current in Amperes or Amps (A) Q: charge in Coulombs (C) Q: charge in Coulombs (C) t: time in seconds (s) t: time in seconds (s)

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Electron Flow In a normal electrical circuit, it is the electrons that carry the charge. In a normal electrical circuit, it is the electrons that carry the charge. So if the electrons one way, which way does the current move? So if the electrons one way, which way does the current move?

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Problem How many electrons per hour flow past a point in a circuit if it bears 11.4 mA of direct current? How many electrons per hour flow past a point in a circuit if it bears 11.4 mA of direct current?

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EMF Cells convert chemical energy into electrical energy. Cells convert chemical energy into electrical energy. The potential difference (voltage) provided by a cell is called its electromotive force (or emf). The potential difference (voltage) provided by a cell is called its electromotive force (or emf). The emf of a cell is constant, until near the end of the cell’s useful lifetime. The emf of a cell is constant, until near the end of the cell’s useful lifetime. Misnomer: The emf is not really a force. Misnomer: The emf is not really a force.

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Battery A battery is composed of more than one cell in series. A battery is composed of more than one cell in series. The emf of a battery is the sum of the emf’s of the cells. The emf of a battery is the sum of the emf’s of the cells.

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Problem If a typical AA cell has an emf of 1.5 V, how much emf do 4 AA cells provide? If a typical AA cell has an emf of 1.5 V, how much emf do 4 AA cells provide? Draw the battery composed of these 4 cells. Draw the battery composed of these 4 cells.

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Circuit Components VoltmeterAmmeter OhmmeterSwitch

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Problem Draw a single loop circuit that contains a cell, a light bulb, and a switch. Draw a single loop circuit that contains a cell, a light bulb, and a switch. Put a voltmeter in the circuit so it reads the potential difference across the light bulb. Put a voltmeter in the circuit so it reads the potential difference across the light bulb.

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Series Series components are put together so that all the current must go through each one Series components are put together so that all the current must go through each one Bulbs in series all have the same current. Bulbs in series all have the same current.

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Parallel Parallel components are put together so that the current divides, and each component gets only a fraction of it. Parallel components are put together so that the current divides, and each component gets only a fraction of it. Bulbs in series do not have the same current Bulbs in series do not have the same current

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Problem Draw a circuit with a cell and two bulbs in series. Draw a circuit with a cell and two bulbs in series.

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Problem Draw a circuit having a cell and four bulbs. Exactly two of the bulbs must be in parallel. Draw a circuit having a cell and four bulbs. Exactly two of the bulbs must be in parallel.

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Mini Lab Draw a circuit containing one cell, one bulb, and a switch. Create this with the available components. Measure the voltage across the cell and then across the bulb. What do you observe? Draw a circuit containing one cell, one bulb, and a switch. Create this with the available components. Measure the voltage across the cell and then across the bulb. What do you observe?

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Mini Lab Draw a circuit containing two cells in series, two bulbs in series, and a switch. Create this with the available components. Draw a circuit containing two cells in series, two bulbs in series, and a switch. Create this with the available components. What do you observe happens to the bulbs when you unscrew one of them? What do you observe happens to the bulbs when you unscrew one of them? Measure the voltage across the battery and across each bulb. What do you observe? Measure the voltage across the battery and across each bulb. What do you observe?

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Mini Lab Draw a circuit containing two cells in series, two bulbs in parallel, and a switch. Create this with the available components. Draw a circuit containing two cells in series, two bulbs in parallel, and a switch. Create this with the available components. What do you observe happens to the bulbs when you unscrew one bulb? What do you observe happens to the bulbs when you unscrew one bulb? Measure the voltage across the battery and across each bulb. What do you observe? Measure the voltage across the battery and across each bulb. What do you observe?

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Ohm’s Law

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Conductors Conduct electricity easily. Conduct electricity easily. Have high “conductivity”. Have high “conductivity”. Have low “resistivity”. Have low “resistivity”. Metals are examples. Metals are examples. Wires are made of conductors Wires are made of conductors

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Insulators Don’t conduct electricity easily. Don’t conduct electricity easily. Have low “conductivity”. Have low “conductivity”. Have high “resistivity”. Have high “resistivity”. Rubber is an example. Rubber is an example.

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Resistors Resistors are devices put in circuits to reduce the current flow. Resistors are devices put in circuits to reduce the current flow. Resistors are built to provide a measured amount of “resistance” to electrical flow, and thus reduce the current. Resistors are built to provide a measured amount of “resistance” to electrical flow, and thus reduce the current.

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Circuit Components Resistor

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Problem Draw a single loop circuit containing two resistors and a cell. Draw voltmeters across each component. Draw a single loop circuit containing two resistors and a cell. Draw voltmeters across each component.

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Resistance Resistance depends on resistivity and on geometry of the resistor. Resistance depends on resistivity and on geometry of the resistor. R = ρL/A R = ρL/A ρ: resistivity (Ω m) ρ: resistivity (Ω m) L: length of resistor (m) L: length of resistor (m) A: cross sectional area of resistor (m 2 ) A: cross sectional area of resistor (m 2 ) Unit of resistance: Ohms (Ω) Unit of resistance: Ohms (Ω)

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Problem What is the resistivity of a substance which has a resistance of 1000 Ω if the length of the material is 4.0 cm and its cross sectional area is 0.20 cm 2 ? What is the resistivity of a substance which has a resistance of 1000 Ω if the length of the material is 4.0 cm and its cross sectional area is 0.20 cm 2 ?

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Problem What is the resistance of a mile of copper wire if the diameter is 5.0 mm? (resistivity of copper is 1.72 x 10 -8 ) What is the resistance of a mile of copper wire if the diameter is 5.0 mm? (resistivity of copper is 1.72 x 10 -8 )

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Ohm’s Law Resistance in a component in a circuit causes potential to drop according to the equation: Resistance in a component in a circuit causes potential to drop according to the equation: ΔV = IR ΔV = IR Δ V: potential drop (Volts) Δ V: potential drop (Volts) I: current (Amperes) I: current (Amperes) R: resistance (Ohms) R: resistance (Ohms)

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Problem Determine the current through a 333-W resistor if the voltage across the resistor is observed to be 1.5 V. Determine the current through a 333-W resistor if the voltage across the resistor is observed to be 1.5 V.

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Problem Draw a circuit with a AA cell attached to a light bulb of resistance 4 W. Determine the current through the bulb. Draw a circuit with a AA cell attached to a light bulb of resistance 4 W. Determine the current through the bulb.

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Ohmmeter Measures Resistance. Measures Resistance. Placed across resistor when no current is flowing. Placed across resistor when no current is flowing.

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Mini Lab Set up your digital multi-meter to measure resistance. Measure the resistance of the each light bulb on your board. Record the results. Set up your digital multi-meter to measure resistance. Measure the resistance of the each light bulb on your board. Record the results. Wire the three bulbs together in series, and draw this arrangement. Measure the resistance of all three bulbs together in the series circuit. How does this Wire the three bulbs together in series, and draw this arrangement. Measure the resistance of all three bulbs together in the series circuit. How does this compare to the resistance of the individual bulbs? compare to the resistance of the individual bulbs? Wire the three bulbs together in parallel, and draw this arrangement. Measure the resistance of the parallel arrangement. How does this compare to the resistance of the individual bulbs? Wire the three bulbs together in parallel, and draw this arrangement. Measure the resistance of the parallel arrangement. How does this compare to the resistance of the individual bulbs?

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Ammeter An ammeter measures current. An ammeter measures current. It is placed in the circuit in a series connection. It is placed in the circuit in a series connection. An ammeter has very low resistance, and does not contribute significantly to the total resistance of the circuit. An ammeter has very low resistance, and does not contribute significantly to the total resistance of the circuit.

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Power P = W/t P = W/t P = ΔE/Δt P = ΔE/Δt Units Units Watts Watts Joules/second Joules/second

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Power in Circuits P = IΔV P = IΔV P: power (W) P: power (W) I: current (A) I: current (A) ΔV: potential difference (V) ΔV: potential difference (V) P = I 2 R P = I 2 R P = (ΔV) 2 /R P = (ΔV) 2 /R

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Problem How much current flows through a 100-W light bulb connected to a 120 V DC power supply? What is the resistance of the bulb? How much current flows through a 100-W light bulb connected to a 120 V DC power supply? What is the resistance of the bulb?

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Problem If electrical power is 5.54 cents per kilowatt hour, how much does it cost to run a 100-W light bulb for 24 hours? If electrical power is 5.54 cents per kilowatt hour, how much does it cost to run a 100-W light bulb for 24 hours?

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Resistors in Circuits Resistors can be placed in circuits in a variety of arrangements in order to control the current. Resistors can be placed in circuits in a variety of arrangements in order to control the current. Arranging resistors in series increases the resistance and causes the current to be reduced. Arranging resistors in series increases the resistance and causes the current to be reduced. Arranging resistors in parallel reduces the resistance and causes the current to increase. Arranging resistors in parallel reduces the resistance and causes the current to increase. The overall resistance of a specific grouping of resistors is referred to as the equivalent resistance. The overall resistance of a specific grouping of resistors is referred to as the equivalent resistance.

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Resistors in Series

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Resistors in Parallel

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Mini Lab What is the equivalent resistance of a 100-Ω, a 330-Ω and a 560-Ω resistor when these are in a series arrangement? (Draw, build a circuit, measure, and calculate. Compare measured and calculated values). What is the equivalent resistance of a 100-Ω, a 330-Ω and a 560-Ω resistor when these are in a series arrangement? (Draw, build a circuit, measure, and calculate. Compare measured and calculated values).

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Kirchoff’s Rules

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Problem Draw a circuit containing, in order (1) a 1.5 V cell, (2) a 100-Ω resistor, (3) a 330-Ω resistor in parallel with a 100-Ω resistor (4) a 560-Ω resistor, and (5) a switch. Draw a circuit containing, in order (1) a 1.5 V cell, (2) a 100-Ω resistor, (3) a 330-Ω resistor in parallel with a 100-Ω resistor (4) a 560-Ω resistor, and (5) a switch. Calculate the equivalent resistance. Calculate the equivalent resistance. Calculate the current through the cell. Calculate the current through the cell. Calculate the current through the 330-Ω resistor. Calculate the current through the 330-Ω resistor.

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Junction Rule Kirchoff’s 1st rule is also called the “junction rule”. Kirchoff’s 1st rule is also called the “junction rule”. The sum of the currents entering a junction equals the sum of the currents leaving the junction. The sum of the currents entering a junction equals the sum of the currents leaving the junction. This rule is based upon conservation of charge. This rule is based upon conservation of charge.

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Loop Rule Kirchoff’s 2nd rule is also referred to as the “loop rule”. Kirchoff’s 2nd rule is also referred to as the “loop rule”. The net change in electrical potential in going around one complete loop in a circuit is equal to zero. The net change in electrical potential in going around one complete loop in a circuit is equal to zero. This rule is based upon conservation of energy. This rule is based upon conservation of energy.

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Ohm’s Law Graph Make a table of current and resistance data and graph the data such that voltage is the slope of a best-fit line. Make a table of current and resistance data and graph the data such that voltage is the slope of a best-fit line. Wire a circuit with a cell and one or more resistors. Wire a circuit with a cell and one or more resistors. Calculate and record the resistance. Calculate and record the resistance. Measure and record the corresponding current. Do this 8 times without duplicating your resistance values. Measure and record the corresponding current. Do this 8 times without duplicating your resistance values. Rearrange the equation ΔV = IR so that ΔV is the slope of a “linear” equation. Rearrange the equation ΔV = IR so that ΔV is the slope of a “linear” equation. Construct a graph from your data that corresponds to this rearranged equation. Construct a graph from your data that corresponds to this rearranged equation. Calculate and clearly report the slope of the line. How does this compare to the emf of 1.5 V for a D-cell? Calculate and clearly report the slope of the line. How does this compare to the emf of 1.5 V for a D-cell?

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Terminal Voltage When a current is drawn from a battery, the voltage across its terminals drops below its rated EMF. When a current is drawn from a battery, the voltage across its terminals drops below its rated EMF. The chemical reactions in the battery cannot supply charge fast enough to maintain the full EMF. The chemical reactions in the battery cannot supply charge fast enough to maintain the full EMF. Thus the battery is said to have an internal resistance, designated r. Thus the battery is said to have an internal resistance, designated r.

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Terminal Voltage and EMF A real battery is then modeled as if it were a perfect emf, ε. in series with a resistor r. A real battery is then modeled as if it were a perfect emf, ε. in series with a resistor r. Terminal voltage V ab Terminal voltage V ab When no current is drawn from the battery, the terminal voltage equals the emf. When no current is drawn from the battery, the terminal voltage equals the emf. When a current I flows from the battery, there is an internal drop in voltage equal to Ir, thus the terminal voltage (actual voltage delivered) is V ab = ε - Ir When a current I flows from the battery, there is an internal drop in voltage equal to Ir, thus the terminal voltage (actual voltage delivered) is V ab = ε - Ir

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