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**Electricity & Magnetism**

Current Electricity: Direct Current Circuits, Ohm’s Law, Resistance, Electric Power, Equivalent Resistance, Kirchoff’s Rules

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**Current Current is defined as the flow of positive charge I = Q/t**

I is current in Amperes (A) Q is charge in Coulombs (C) t is time in seconds (s) In a normal electric circuit, electrons move to carry charge – the current is opposite from the movement of electrons

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Practice #1 How many electrons per hour flow past a point in a circuit if it bears 11.4 mA of direct current? If the electrons are moving north, which way is the current?

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Sample problem How many electrons per hour flow past a point in a circuit if it bears 11.4 mA of direct current? If the electrons are moving north, in which direction is the current?

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**Cells Cells convert chemical energy into electrical energy**

The potential difference (voltage) provided by a cell is called its electromotive force (emf) The emf of a cell is constant until near the end of the cell’s useful lifetime The emf is not really a force! It’s one of the biggest misnomers in physics!

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Cells cell battery

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**Battery 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 Practice Problem #2: 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.

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Sample problem 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.

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**Circuit Components Ω Light bulb: Wire: Switch:**

Voltmeter: (measures voltage) Ohmmeter: (measures resistance) Ammeter (measures current) Ω

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Circuit Practice - #3 Draw a single loop circuit that contains a cell, a light bulb, and a switch. Name the components.

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Sample problem Draw a single loop circuit that contains a cell, a light bulb, and a switch. Name the components bulb cell switch

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#4 Now put a voltmeter in the circuit so it reads the potential difference across the bulb

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**Series arrangement of components**

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

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**Parallel arrangement of components**

Parallel components are put together so that the current divides, and each component gets only a fraction of it. I 1/3 I Three bulbs in parallel

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Practice # 5-6 5. Draw a circuit with one cell and two bulbs in series. 6. Draw a circuit having a cell and four bulbs. Exactly two of the bulbs must be in parallel.

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Sample problem Draw a circuit with a cell and two bulbs in series.

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

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**Conductors & Insulators**

Conduct electricity easily Have high “conductivity” Have low “resistivity” Metals are examples Wires are made of conductors Don’t conduct electricity easily Have low “conductivity” Have high “resistivity” Rubber is an example

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Resistors 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

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

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Sample problem Draw a single loop circuit containing two resistors and a cell. Draw voltmeters across each component. V

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Resistance, R Resistance depends on resistivity and on geometry of the resistor R = ρL/A ρ : resistivity (Ωm) from the material L: length of resistor (m) A: cross sectional area of resistor (m2) Unit of resistance: Ohms (Ω)

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Practice #8 What is the resistivity of a substance which has resistance of 1000 Ω if the length of the material is 4.0 cm and its cross sectional area is 0.20 cm2?

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Sample problem What is the resistivity of a substance which has a resistance of 1000 W if the length of the material is 4.0 cm and its cross sectional area is 0.20 cm2?

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#9 What is the resistance of a mile of copper wire if the diameter is 10.0 mm? (resistivity of copper is 1.72 x 10-8 Ωm)

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Sample problem What is the resistance of a mile of copper wire if the diameter is 10.0 mm?

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

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Practice #10 Determine the current through a 333 Ω resistor if the voltage across the resistor is observed to be 1.5 V.

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Sample problem 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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Practice #11 Draw a circuit with a AA cell attached to a light bulb of resistance 4 Ω. Determine the current through the bulb.

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Sample problem Draw a circuit with a AA cell attached to a light bulb of resistance 4 W. Determine the current through the bulb. (Calculate)

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**Ohmmeter Measures Resistance.**

Placed across resistor when no current is flowing. W

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**Ammeter An ammeter measures current**

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

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**Power In General In Electrical Circuits P = W/t P = ΔE/Δt Units:**

Watts Joules/second P = I Δ V P: Power (W) I: Current (A) Δ V: Potential difference (V) P = I2R P = (Δ V)2/R

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Practice #12 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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Sample 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?

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#13 If electrical energy (power x time) 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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Sample 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?

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Resistors in circuits 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 the 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

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**Equivalent Resistance**

In Series In Parallel Req = R1 + R2 + R3… ΣReq = Ri 1/Req = 1/R1 + 1/R2 + 1/R3… 1/Req = Σ(1/Ri)

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**Kirchoff's 1st Rule 3.0 A I4 4.0 A 1.5 A Practice Problem #15**

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 This rule is based upon conservation of charge Find the current I4 (magnitude and direction) 3.0 A I4 4.0 A 1.5 A

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Kirchoff's 2nd 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. This rule is based upon the conservation of energy

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Practice Problem #16 Use the loop rule to determine the potential drop across the light bulb.

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**Capacitors in Circuits**

+Q -Q +Q -Q

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**Equivalent Capacitance**

series Charge is same on all capacitors in series arrangement. 1/Ceq = 1/C1+ 1/C2 + 1/C3

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**Equivalent Capacitance**

parallel Voltage is same on all capacitors in parallel arrangement. Ceq = C1+ C2 + C3

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**Mini-Lab J Draw and construct the following circuit.**

Predict all 3 currents. Apply Kirchoff’s 1st Rule to your current measurements Measure the voltage across all components. Apply Kirchoff’s 2nd Rule to your voltage measurements.

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Mini-Lab K Draw and construct a circuit containing a cell and one 330-Ω resistor. Measure the potential drop across the resistor Measure the current through the resistor Does ΔV = IR? I (A) R(Ω) ΔV(V) calculated Measured Difference (V)

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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 Wire a circuit with a cell and one or more resistors. Calculate and record the resistance. Measure and record the corresponding current. Do this 8 times without duplicating your resistance values. You will have to use resistor combinations in addition to single resistors. Rearrange the equation V = IR so that V is the slope of a “linear” 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 a 1.5 V for a D-cell?

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Circuit Mini-Lab A Draw a circuit containing one cell, one bulb, and a switch. Wire this circuit. Measure the voltage across the cell and across the bulb. What do you observe?

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Mini-Lab B Draw a circuit containing two cells in series, one bulb, and a switch. Wire this on your circuit board. What do you observe happens to the bulb: With two cells instead of one? When opening and closing the switch? Measure the voltage across the battery and across the bulb. What do you observe?

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Mini-Lab C Draw a circuit containing two cells in series, two bulbs in series, and a switch. Wire this on your circuit board. 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?

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Mini-Lab D Draw a circuit containing two cells in series, two bulbs in parallel, and a switch. Wire this on your circuit board. 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?

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**General Rules for Circuits**

How does the voltage from a cell or battery get dispersed in a circuit: When there is one component? When there are two components in series? When there are two components in parallel?

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

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Mini-Lab F Measure the resistance of the different resistors you have been given. Make a table and record the color of the first three bands (ignore the silver/gold band) and the resistance associated with the band color. See if you can figure out the code.

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**Resistor codes Resistor codes are read as follows:**

It is helpful to know the code, but you will not be required to memorize it

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Mini-Lab G What is the equivalent resistance of a 100-Ω, a 330- Ω, and a 82- Ω resistor when these are in a series arrangement? Draw the circuit Build the circuit Measure values Calculate and compare measured and calculated values

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Mini-Lab H What is the equivalent resistance of a 100-Ω, a 330-Ω, and a 82-Ω resistor when these are in a parallel arrangement? Draw Build the circuit Measure Calculate and compare values

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Mini-Lab I Draw and build an arrangement of resistance that uses both parallel and series arrangements for 5 or 6 resistors in your kit. Calculate and then measure the equivalent resistance. Compare the values.

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#14 Draw a circuit containing, in order (1) a 1.5 V cell, (2) a 68-Ω resistor, (3) a 330-Ω resistor in parallel with a 100-Ω resistor, (4) an 82-Ω resistor, and (5) a switch. Calculate the equivalent resistance Calculate the current through the cell Calculate the current through the 330-Ω resistor

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