Electric Circuits Electric potential difference Electromotive force- emf Circuits Conductors and resistors Resistivity and Resistance Circuit Diagrams Electric Current & DC Circuits Measurement

1. Electric Potential Difference 1). Electric Potential Energy

1). Potential Energy In electric field:

1). electric Potential Energy When E is uniform:

The potential energy per unit charge is called the electric potential.   The potential energy per unit charge is called the electric potential. And : Electric Potential Difference is: SI Unit of Electric Potential: joule/coulomb = volt (V)

19.2 The Electric Potential Difference DEFINITION OF ELECTRIC POTENTIAL The electric potential at a given point is the electric potential energy of a small test charge divided by the charge itself: SI Unit of Electric Potential: joule/coulomb = volt (V)

2). The Electric Potential Difference The Accelerations of Positive and Negative Charges A positive test charge is released from A and accelerates towards B. Upon reaching B, the test charge continues to accelerate toward C. Assuming that only motion along the line is possible, what will a negative test charge do when released from rest at B?

  A positive charge accelerates from a region of higher electric potential toward a region of lower electric potential. A negative charge accelerates from a region of lower potential toward a region of higher potential.

The Electric Field and Potential Are Related

2. Electromotive Force – emf emf – is the voltage developed by any source of electrical energy such as a battery or dynamo. It is generally defined as the potential for a source in a circuit.  measured in volts

2. Electromotive Force from Electric battery- Voltage Various cells and batteries (top-left to bottom-right): two AA, one D, one handheld ham radiobattery, two 9-volt (PP3), two AAA, one C, onecamcorder battery, one cordless phone battery. The symbol for a battery in a circuit diagram. It originated as a schematic drawing of the earliest type of battery, a voltaic pile. Line art drawing of a dry cell: 1. brass cap, 2. plastic seal, 3. expansion space, 4. porous cardboard, 5. zinc can, 6. carbon rod, 7. chemical mixture.

The SI unit on electric potential difference is the volt,  V (in honor of Alessandro Volta).  Within the electrochemical cells of the battery, there is an electric field established between the two terminals, directed from the positive terminal towards the negative terminal.  The negative terminal is described as the low potential terminal.

How battery works: In a battery-powered electric circuit, the chemical energy is used to do work. Chemical energy is transformed into electric potential energy within the internal circuit (i.e., the battery). Once at the high potential terminal, a positive test charge will then move through the external circuit and do work upon the light bulb or the motor or the heater coils. The positive test charge returns to the negative terminal at a low energy and low potential, ready to repeat the cycle (or should we say circuit) all over again.

3. Circuits An electric circuit is an external path that charges can follow between two terminals using a conducting material.

1). Requirements  the path must be complete and unbroken--There must be a closed conducting loop in the external circuit that stretches from the high potential, positive terminal to the low potential, negative terminal. The Requirement of an Energy Supply--There must be an energy supply capable doing work on charge to move it from a low energy location to a high energy location and thus establish an electric potential difference across the two ends of the external circuit.

Electromotive Force and Current In an electric circuit, an energy source and an energy consuming device are connected by conducting wires through which electric charges move.

2). Symbols for circuit elements A Ideal conductor - generally assume that that R=0 Ideal EMF NOTE – device is asymmetric Ideal Resistor EMF with internal resistance Ideal Voltmeter - generally assume that that R=∞ - No current flows through an ideal voltmeter – Ideal Ammeter - generally assume that that R=0 Electrically, an ideal ammeter is a perfect conductor

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Electromotive Force and Current Within a battery, a chemical reaction occurs that transfers electrons from one terminal to another terminal. The maximum potential difference across the terminals is called the electromotive force (emf). emf give circuit voltage supply which is represented by V

Batteries and Current The battery pushes current through the circuit. A battery acts like a pump, pushing charge through the circuit. It is the circuit's energy source. Charges do not experience an electrical force unless there is a difference in electrical potential (voltage).Therefore, batteries have a potential difference between their terminals. The positive terminal is at a higher voltage than the negative terminal.

3). Electric Current The electric current is the amount of charge per unit time that passes through a surface that is perpendicular to the motion of the charges. One coulomb per second equals one ampere (A).

Current, resistance and electromotive force Current is a concept with wide spread applications describing the rate of flow of some quantity that can be: -Throughput of cars per time interval: -water volume coming out of a hose per time interval:

20.1 Electromotive Force and Current If the charges move around the circuit in the same direction at all times, the current is said to be direct current (dc). If the charges move first one way and then the opposite way, the current is said to be alternating current (ac).

20.1 Electromotive Force and Current Example 1 A Pocket Calculator The current in a 3.0 V battery of a pocket calculator is 0.17 mA. In one hour of operation, (a) how much charge flows in the circuit and (b) how much energy does the battery deliver to the calculator circuit? (a) (b)

20.1 Electromotive Force and Current Conventional current is the hypothetical flow of positive charges that would have the same effect in the circuit as the movement of negative charges that actually does occur.

Electron's journey through a circuit In the wires of electric circuits, an electron is the actual charge carrier. zigzag path that results from countless collisions with the atoms of the conducting wire

Conductor’s Resistance Some conductors "conduct" better or worse than others. Reminder: conducting means a material allows for the free flow of electrons. The flow of electrons is just another name for current. Another way to look at it is that some conductors resist current to a greater or lesser extent. We call this resistance, R. Resistance is measured in ohms which is noted by the Greek symbol omega (Ω)

Demo http://phet.colorado.edu/en/simulations/category/physics/electricity-magnets-and-circuits Battery - resistor circuit Circuit Construction Kit (DC Only)

Eg1. 12 C of charge passes a location in a circuit in 10 seconds. What is the current flowing past the point? Eg2. A circuit has 10 A of current.H ow long does it take 20C of charge to travel through the circuit?

Eg3. 20 C of charge passes a location in a circuit in 30 seconds. What is the current flowing past the point? eg4. A circuit has 10 A of current. How much charge travels through the circuit after 20s?

Eg5. A circuit has 3 A of current. How long does it take 45 C of charge to travel through the circuit? eg6 A circuit has 2.5 A of current. How much charge travels through the circuit after 4s?

Basic Circuits The circuit cannot have gaps. The bulb had to be between the wire and the terminal. A voltage difference is needed to make the bulb light. The bulb still lights regardless of which side of the battery you place it on.

4. Ohm’s Law The resistance (R) is defined as the ratio of the voltage V applied across a piece of material to the current I through the material.

The ratio V/I is a constant, where V is the 4. Ohm’s Law OHM’S LAW The ratio V/I is a constant, where V is the voltage applied across a piece of material and I is the current through the material: SI Unit of Resistance: volt/ampere (V/A) = ohm (Ω)

To the extent that a wire or an electrical 4 Ohm’s Law To the extent that a wire or an electrical device offers resistance to electrical flow, it is called a resistor.

The filament in a light bulb is a resistor in the form 4 Ohm’s Law Example 1 A Flashlight The filament in a light bulb is a resistor in the form of a thin piece of wire. The wire becomes hot enough to emit light because of the current in it. The flashlight uses two 1.5-V batteries to provide a current of 0.40 A in the filament. Determine the resistance of the glowing filament.

2. A flashlight has a resistance of 30 Ω and is connected by a wire to a 90 V source of voltage. What is the current in the flashlight? 3. What is the current in a wire whose resistance is 3 Ω if 1.5 V is applied to it?

How much voltage is needed in order to produce 5. How much voltage is needed in order to produce a 0.70 A current through a 490 Ω resistor? 6. How much voltage is needed in order to produce a 0.5 A current through a 150 Ω resistor?

7. What is the resistance of a rheostat coil, if 0.05 A of current flows through it when 6 V is applied across it? 8. What is the resistance of a rheostat coil, if 20 A of current flows through it when 1000 V is applied across it?

5 Resistance and Resistivity For a wide range of materials, the resistance of a piece of material of length L and cross-sectional area A is resistivity in units of ohm·meter the measure of a conductor's resistance to conduct is called its resistivity. Each material has a different resistivity. Resistivity is abbreviated using the Greek letter rho (ρ). Combining what we know about A, L, and ρ, we can find a conductor's total resistance.

Resistance, R, is measured in Ohms (Ω). Ω is the Greek letter Omega. Cross-sectional area, A, is measured in m2 Length, L, is measured in m Resistivity, ρ, is measured in Ωm

5 Resistance and Resistivity

What is the resistance of a good conductor? Low; low resistance means that electric charges are free to move in a conductor.

Check: Rank the following materials in order of best conductor to worst conductor. A Iron, Copper, Platinum B Platinum, Iron, Copper C Copper, Iron, Platinum

5 Resistance and Resistivity Example 3 Longer Extension Cords The instructions for an electric lawn mower suggest that a 20-gauge extension cord can be used for distances up to 35 m, but a thicker 16-gauge cord should be used for longer distances. The cross sectional area of a 20-gauge wire is 5.2x10-7Ω·m, while that of a 16-gauge wire is 13x10-7Ω·m. Determine the resistance of (a) 35 m of 20-gauge copper wire and (b) 75 m of 16-gauge copper wire. (a) (b)

3. What is the resistance of a 2 m long copper wire whose cross-sectional area of 0.2 mm2? 4. An aluminum wire with a length of 900 m and cross sectional area of 10 mm2 has a resistance of 2.5 Ω. What is the resistivity of the wire?

6. What is the cross-sectional area of a 10Ω copper wire of length is 10000 meters ? 7. What is the length of a 10 Ω copper wire whose diameter is 3.2 mm?

20.3 Resistance and Resistivity Impedance Plethysmography.

20.3 Resistance and Resistivity temperature coefficient of resistivity

between the battery terminals is V. 20.4 Electric Power Consider the charge ∆q flowing through a battery where the potential difference between the battery terminals is V. energy power time

6. Electric Power ELECTRIC POWER When there is current in a circuit as a result of a voltage, the electric power delivered to the circuit is: SI Unit of Power: watt (W) Many electrical devices are essentially resistors:

Electric circuits are similar. Electrical Power Let's think about this another way... The water at the top has GPE & KE. As the water falls, it loses GPE and the wheel gets turned, doing work. When the water falls to the bottom it is now slower, having done work. Electric circuits are similar. A charge falls from high voltage to low voltage. In the process of falling energy may be used (light bulb, run a motor, etc).

Example 5 The Power and Energy Used in a Flashlight Electric Power Example 5 The Power and Energy Used in a Flashlight In the flashlight, the current is 0.40A and the voltage is 3.0 V. Find (a) the power delivered to the bulb and (b) the energy dissipated in the bulb in 5.5 minutes of operation.

20.4 Electric Power (a) (b)

2. A toy car's electric motor has a resistance of 17 Ω; find the power delivered to it by a 6-V battery. 3. A toy car's electric motor has a resistance of 6 Ω; find the power delivered to it by a 7-V battery.

4. What is the power consumption of a flash light bulb that draws a current of 0.28 A when connected to a 6 V battery? 5. What is the power consumption of a flash light bulb that draws a current of 0.33 A when connected to a 100 V battery?

6. A 30Ω toaster consumes 560 W of power: how much current is flowing through the toaster? 7. A 50Ω toaster consumes 200 W of power: how much current is flowing through the toaster?

8. When 30 V is applied across a resistor it generates 600 W of heat: what is the magnitude of its resistance? 9. When 100 V is applied across a resistor it generates 200 W of heat: what is the magnitude of its resistance?

Circuit Diagrams *Note: Circuit diagrams do not show where each part is physically located.

7. Series Wiring There are many circuits in which more than one device is connected to a voltage source. Series wiring means that the devices are connected in such a way that there is the same electric current through each device.

Series Wiring Series resistors

Example 8 Resistors in a Series Circuit Series Wiring Example 8 Resistors in a Series Circuit A 6.00 Ω resistor and a 3.00 Ω resistor are connected in series with a 12.0 V battery. Assuming the battery contributes no resistance to the circuit, find (a) the current, (b) the power dissipated in each resistor, and (c) the total power delivered to the resistors by the battery.

Series Wiring (a) (b) (c)

Personal electronic assistants. Series Wiring Personal electronic assistants.

8. Parallel Wiring Parallel wiring means that the devices are connected in such a way that the same voltage is applied across each device. When two resistors are connected in parallel, each receives current from the battery as if the other was not present. Therefore the two resistors connected in parallel draw more current than does either resistor alone.

Parallel Wiring

The two parallel pipe sections are equivalent to a single pipe of the Parallel Wiring The two parallel pipe sections are equivalent to a single pipe of the same length and same total cross sectional area.

Parallel Wiring parallel resistors

Example 10 Main and Remote Stereo Speakers Parallel Wiring Example 10 Main and Remote Stereo Speakers Most receivers allow the user to connect to “remote” speakers in addition to the main speakers. At the instant represented in the picture, the voltage across the speakers is 6.00 V. Determine (a) the equivalent resistance of the two speakers, (b) the total current supplied by the receiver, (c) the current in each speaker, and (d) the power dissipated in each speaker.

Parallel Wiring (a) (b)

Parallel Wiring (c) (d)

Conceptual Example 11 A Three-Way Light Bulb and Parallel Wiring Within the bulb there are two separate filaments. When one burns out, the bulb can produce only one level of illumination, but not the highest. Are the filaments connected in series or parallel? How can two filaments be used to produce three different illumination levels?

9. Circuits Wired Partially in Series and Partially in Parallel

is called internal resistance. Batteries and generators add some resistance to a circuit. This resistance is called internal resistance. The actual voltage between the terminals of a batter is known as the terminal voltage.

Example 12 The Terminal Voltage of a Battery 20.9 Internal Resistance Example 12 The Terminal Voltage of a Battery The car battery has an emf of 12.0 V and an internal resistance of 0.0100 Ω. What is the terminal voltage when the current drawn from the battery is (a) 10.0 A and (b) 100.0 A? (a) (b)

20.10 Kirchhoff’s Rules The junction rule states that the total current directed into a junction must equal the total current directed out of the junction.

20.10 Kirchhoff’s Rules The loop rule expresses conservation of energy in terms of the electric potential and states that for a closed circuit loop, the total of all potential rises is the same as the total of all potential drops.

Junction rule. The sum of the magnitudes of the currents directed 20.10 Kirchhoff’s Rules KIRCHHOFF’S RULES Junction rule. The sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of a junction. Loop rule. Around any closed circuit loop, the sum of the potential drops equals the sum of the potential rises.

Example 14 Using Kirchhoff’s Loop Rule 20.10 Kirchhoff’s Rules Example 14 Using Kirchhoff’s Loop Rule Determine the current in the circuit.

20.10 Kirchhoff’s Rules

20.10 Kirchhoff’s Rules

Applying Kirchhoff’s Rules Reasoning Strategy Applying Kirchhoff’s Rules Draw the current in each branch of the circuit. Choose any direction. If your choice is incorrect, the value obtained for the current will turn out to be a negative number. Mark each resistor with a + at one end and a – at the other end in a way that is consistent with your choice for current direction in step 1. Outside a battery, conventional current is always directed from a higher potential (the end marked +) to a lower potential (the end marked -). Apply the junction rule and the loop rule to the circuit, obtaining in the process as many independent equations as there are unknown variables. 4. Solve these equations simultaneously for the unknown variables.

20.11 The Measurement of Current and Voltage A dc galvanometer. The coil of wire and pointer rotate when there is a current in the wire.

20.11 The Measurement of Current and Voltage An ammeter must be inserted into a circuit so that the current passes directly through it.

20.11 The Measurement of Current and Voltage If a galvanometer with a full-scale limit of 0.100 mA is to be used to measure the current of 60.0 mA, a shunt resistance must be used so that the excess current of 59.9 mA can detour around the galvanometer coil.

20.11 The Measurement of Current and Voltage To measure the voltage between two points in a circuit, a voltmeter is connected between the points.

20.12 Capacitors in Series and Parallel Parallel capacitors

20.12 Capacitors in Series and Parallel Series capacitors

20.13 RC Circuits Capacitor charging time constant

20.13 RC Circuits Capacitor discharging time constant

20.13 RC Circuits

20.14 Safety and the Physiological Effects of Current To reduce the danger inherent in using circuits, proper electrical grounding is necessary.