Electric Energy and Circuits Chapter 15

Potential Difference Recall potential energy – the amount of energy an object could have due to its position. Ex. A book on a desk vs on the floor, a sky diver on the ground or 5000 ft in the air. The potential to move implies stored energy. For an electric current to operate there must be a difference in the amount of energy.

The electric potential difference between any two points in a circuit is the quotient of the change in the electric potential energy of charges passing between those points and the quantity of the charge. Electric potential difference - V or volt Change in electrical potential energy - ΔEQ, measured in joules Charge - q measured in Coulombs

One joule per coulomb is equal to one volt. Recall from Physics 521 work and energy are interchangeable. Work = ΔEnergy

Variations of the formula for finding the electric potential difference. 1 Volt = 1 Newton-meter/Coulomb = J/C

Do Sample Problem on Page 691 Do Practice Problems on Page 692 #s 1-3

Electric Current When the ends of a conductor are at different potentials (voltage), charge flows from the region of higher potential to the region of lower potential across the ends of the conductor. The flow of charges will continue until both ends of the conductor reach the same potential, at which time it will stop flowing.

To continue a flow of charge in a conductor, a difference of potential must be maintained across the ends of the conductor. This requirement is provided by an “power supply” (for example, a battery converts chemical energy into electrical energy; a solar cell converts light energy into electric energy; a generator converts mechanical energy into electrical energy).

External energy from the pump sets up a potential difference between the two ends of the conductor by maintaining a constant negative charge in one area and a constant positive charge in another area (terminals of a battery). If these 2 points, at a different potential, are connected by a conducting wire, electric charge will flow from an area of high potential energy to the area of low potential energy within a closed loop called an electric circuit.

A circuit consists of a device which continuously increases the PE of the charges (power supply) connected to a device (load) that continuously reduces the PE of the charges by providing resistance to their movement (i.e. electric motor). This loss of PE of the charges as they move through the circuit can be converted into other forms of energy (i.e. a motor converts electric energy into kinetic energy and a lamp converts electric energy into light energy).

Electric pumps do not create electric charges or electrons, but only provide energy to move them through a circuit. The total amount of charge or energy in a circuit never changes; it is conserved. In any circuit, the PE increase (qV) provided by the charge pump (battery) equals the PE decrease as the current moves through a resistance (i.e. motor) because of the Law of Conservation of Energy.

When the flow takes place in one direction, it is called direct current (DC); and when it flows back and forth it is called alternating current (AC). open circuit- there is a break somewhere in the circuit which prevents current from flowing (i.e. an open switch). closed circuit- all connections are complete and current flows.

Current vs Electron Flow Early concepts (early 1800s) of current electricity “assumed” a positive current. JJ Thomson discovered the electron in 1901 and then scientists realized that it was the negative electron that was moving. However, current (I) means the flow of positive charges from anode (+) to cathode (-) in a circuit. The electron flow is from cathode (-) to anode (+).

The electric current is the flow of charges per unit of time. Current – I measured in amperes (A) Charge – q measured in coulombs (C) Time interval – Δt measured in seconds (s)

Do Sample Problem on Page 695 Do Practice Problems on Page 696 #s 4-11

Current and the Elementary Charge Current is the flow of charges. Elementary charge (e) is the amount of charge on 1 electron – 1.60 × 10-19 C. (Also the proton is + 1.60 × 10-19 C.) q = Ne Do Model Problem on Page 699 Do Practice Problems on Page 700 #s 12-15

Electric Circuits Schematic diagram- diagram of an electric circuit using standard symbols for the electric circuit components (Figs. 15.10-15.12 on Page 701). See Conceptual Problems on Page 702

Steps for Drawing Schematic Diagrams 1. Draw the battery symbol on the left side of the page; put the positive terminal on top. 2. Draw a wire connecting the conventional current out of the positive terminal. When you reach a resistor or another device, draw the symbol for it. 3. If you reach a point where there are 2 or more current paths (i.e. a voltmeter), draw in the diagram and follow one path until the two paths join again, then draw the second path. 4. Follow the path until you get to the negative terminal of the battery. 5. Check your drawing to ensure you have included all parts and that the current paths are complete. The direction of current flow is the direction that positive charges would move (this is called conventional current).

Types of Electric Circuits Series Circuit- a method of connecting all circuit elements (loads and power source) which provides only one path through which current can flow. Parallel Circuit- a method of connecting two or more circuit elements between 2 points which provides more than one current path.

Ammeters and Voltmeters An ammeter, which measures the amount of current, must be connected in series (same path as everything else) to give an accurate reading of current flow. A voltmeter, which measures the potential difference across a circuit device, must be attached in parallel (with one terminal on each side of the device across which it is measuring the potential difference). The potential difference across the device equals the potential difference across the voltmeter. See Figure 15.13 on Page 703

Resistance Section 15.3 Voltage is an electrical pressure that can produce current (a flow of charge) within a conductor. The amount of current that will flow in a circuit depends on the potential difference (voltage) across the circuit and the resistance the conductor (circuit) provides the moving charges.

Resistance (R) - the obstruction or resistance to the flow of electrical charges in a circuit. Fixed Resistor- a device designed to have a specific resistance. It is used to control the current in circuits or parts of circuits. Variable Resistor- also called a rheostat or potentiometer- a device consisting of a coil of resistance wire and a sliding contact point. This allows for varied amounts of current to flow in the circuit according to the equation V = IR. Ex: fans with different speeds and dimming lights.

Factors Affecting Resistance in Electric Conductors Resistance increases proportionately with the length. Resistance varies inversely as the cross- sectional area.

By combining these proportionalities and using the resistivity constant, we get the following equation for the resistance of a conductor: Resistance is measured in ohms. Resistivity() - measured in ∙m (See Table 15.1)

The resistance of a conductor also depends on the conductivity of material used and its temperature (a short, thick, cold conductor reduces resistance). Note that superconductors have zero resistance and therefore, no voltage drop across them.

Do Sample Problem on Page 707 Do Practice Problems on Page 708 #s 16 - 20

Ohm’s Law Ohm’s Law states that the resistance of an object is constant and independent of the voltage across it....the potential difference across a load equals the product of the current through the load and the resistance of the load (limited to metal conductors at stable temperatures).  

Ohm (Ω)- resistance of a device that allows current of 1 amp to flow when a potential difference of 1 volt is applied across the resistance. 1 Ω= 1Volt/Amp Ohm’s Law means that the current in a circuit , kept at a constant temperature, is directly proportional to the voltage across a circuit and inversely proportional to the resistance of the circuit. Therefore, the greater the voltage, the greater the current and the greater the resistance, the lesser the current.

Since I = V/R, the current flowing through a circuit can be regulated in 2 ways: 1. increase or decrease the voltage across the circuit (i.e. to get a stronger charge pump or use more batteries). 2. increase or decrease the resistance of the circuit using devices called resistors. If a device doesn’t obey Ohm’s Law, the graph of I versus V is non-linear (non-ohmic).

Do Sample Problem on Page 713 Do Practice Problems on Page 714 #s 21 - 26

Series and Parallel Circuits Section 15.4 Series Circuit – a complete path for current to flow in which the electrical devices form a single path. Parallel Circuit –a circuit in which there are 2 or more paths for current to flow.

Series Circuits A break anywhere in the path stops current flow in the entire circuit. The total resistance of the circuit equals the sum of the individual resistors. The current (I) equals the voltage provided by the source (V) divided by the total resistance (R). The voltage drop (potential difference) across each device is proportional to its resistance since more energy is needed to move charges through a large resistance. (V=IR)

The sum of the voltage drops across the resistance of each device is equal to the total voltage supplied by the source. V = V1 + V2 + V3 + ... + VN (VN to represent any number of sources) Since V = IR Then V= IR1 + IR2 + IR3 + ... + IRN So then V = I(R1 + R2 + R3 + ... + RN) Therefore I = V/(R1 + R2 + R3 + ... + RN)

The same current will exist in a series circuit with a single resistor that has a resistance equal to the sum of the individual resistances. The number of electrons moving or flowing (I) does not change. Equivalent resistance (Req) – a single resistance that has the same effect as a number of resistances in a series circuit. It is larger than any single resistance. Req = R1 + R2 + R3 + ... + RN

To find the current with multiple resistors you should first find Req then use I = V/Req. The net change in electrical potential around the series circuit must be zero. The charge pump increases the PE of the charges but each resistor decreases the PE of the charges. This results in a net electrical potential change of zero.

To find the potential drop across each resistor in series you must use the equivalent resistance (Req) to find current (I), then you multiply I by the resistance of each individual device to find the potential drop across each device.

Do Model Problem on Page 718 Do Practice Problems on Page 719 - 720 #s 27-31

Parallel Circuits The potential difference across each path is the same because each device connects the same two points of the parallel circuit. The total current is divided among the parallel branches. Current passes more readily into low resistors so that current (I) is inversely proportional to R (smaller R, more I). I = V/R The total current is the sum of the currents through each path. I = I1 + I2 + I3

As the number of parallel branches increases, the overall resistance of the circuit decreases. To find the current through each branch: I1 = V/R1 To find the total current: I = V/R1 + V/R2 + V/R3 I = V(1/R1 + R2 + R3)

Equivalent resistance (1/Req) of three parallel resistors: The Req in a parallel circuit is less than the resistance of any resistor in the circuit.

Do Model Problem on Page 722-724 Do Practice Problems on Page 724 #s 32-35

Electric Circuit Overloads An electric circuit overload may occur when too many current drawing devices are connected in parallel. The overall resistance is reduced with each device added in parallel, so more current is allowed to flow. This adds sufficient thermal energy which may melt insulation on wires causing a short circuit when bare wires touch.

Short Circuit - a very low resistance connection between 2 points in a circuit where the resistance should be very high. Fuse – a safety device, added in series, which melts to stop current flow when it becomes too large. Circuit Breaker – an automatic switch that opens when the current meets a certain value. If a current that is greater than the set value flows, then it will overload and the circuit breaker opens to stop all current flow.

Series – Parallel Combination Circuits Steps If any resistors are in parallel, calculate the equivalent resistance that would replace them. If any equivalent resistors are now connected in series, calculate a new equivalent resistance that can replace them. Repeat steps 1 & 2 until you can reduce the circuit to 1 resistor then find the current through the entire circuit. Finally, the voltage drops and current through each resistor can be found.

Diagrams Series Circuit Parallel Circuit

Recall definitions of ammeters and voltmeters. In an ammeter, the resistance should be as low as possible so it does not change the current. In a voltmeter, the resistance should be high so the current does not go through the voltmeter.

Do Your Ohmwork (worksheet) True/False worksheet Do Sample Problem on Pages 725- 727 Do Practice Problems on Page 728 #s 36 & 37

Energy Transfer in Electric Circuits As we have seen earlier, electrical energy can be transferred into other forms of energy. Electrical power (the power of an electrical appliance) measures the rate at which electric charge or energy is transferred in a circuit (rate appliance does work). For resistors that obey Ohm’s Law, power equals the potential difference (Volts) across a circuit multiplied by the current (Amps).

When a battery converts one Joule of chemical energy to electrical energy per second, then the rate of transfer (power) is 1 J/s or 1 Watt (W). Power is determined by multiplying the potential difference across the appliance (V) by the current (I) moving through the appliance expressed in a term called Watts (J/s).

Power = voltage x current (P = IV) Power (P) measured in Watts (W) Potential difference (V) measured in volts (V) Current (I) measured in amps (A)

Do Sample Problem on Page 736 Do Practice Problems on Page 737 #s 40 -42

Also: P = VI and V = IR, So by substitution: P = I × I × R or P = I2R Or P = VI and I =V/R, So P = V × V/R or P = V2/R

This means that the power lost in a resistor is directly proportional to the square of the current that passes through it and its resistance. The energy is changed from electrical into thermal energy and the resistor gets hot (ex. Heater). The electrical energy transferred to a resistor in a time interval (t) is equal to E = I2Rt.

If all the electric energy is transferred into thermal energy of the resistor, the increase in thermal energy is given by: E = I2Rt or E = Pt. This energy is expressed in Joules. If not all the energy is transferred into thermal energy, then figure out how much by using % efficiency.

Do Model Problem on Page 742 Do Practice Problems on Page 744 #s 46-50

Transmitting Electric Energy In order to transmit energy over long distances, the energy lost to heat (P=I2R) must be controlled. To minimize this loss, there must be a reduction in the current (I) and/or the resistance (R). Since P = VI and the loss of power to heat is proportional to I2, in order to maintain large amounts of electrical power in transmission lines low current (I) at high voltage (V)is required.

Consumer energy cost –the cost of energy to use electrical devices. It is equal to the devices rate of consumption (J/s or W) multiplied by the number of seconds it was used. This gives Joules of energy. Rather than use this small unit of energy, electric companies measure energy consumption in kilowatt hours. Kilowatt hour – the unit of electric energy which is equal to 1000 Watts delivered for 1 hour or 1000 Watts in 3600 seconds. 1kWh = 1000 J/s × 3600 s = 3.6 × 106 J

Do Model Problem on Page 745 Do Practice Problems on Page 746 #s 51-53

Chapter 15 Review Do #s 1, 2, 3, 5, 6, 7, 10, 14, 21, 23-27, & 31 on Pages 747 -749