CIRCUITS

1. CIRCUITS M. Dimler AP Physics B

2. Circuits • Energy stored in an electric field can cause bulk charge flow through conducting materials • A Circuit is a system of conductors and components forming a complete path (closed loop path) for current to travel. Simply put, a Circuit is any path that will allow charge to flow. • Electric charge flowing through a wire is called Current. • An electrical Circuit is built to control Current. • We will learn how to predict the effects of Current flow.

3. Circuits Properties of an electrical circuit include Current Amps A Resistance Ohms Ω Voltage Volts V

4. Current • The rate of charge flow (Current) is the quantity of charge moving through a cross-sectional area per unit time. • In more mathematical terms, I = ΔQ/Δt • Units of Current are Amperes, or Amps, which is a Coulomb/sec • The symbol for Current is I and the symbol for the units of Current is A. • Current is distinguished from drift velocity, or average speed of a charge through a conductor.

5. Current Flow Conventional Current assumes that current flows out of the positive side of the battery, through the circuit, and back to the negative side of the battery. This was the convention established when electricity was first discovered, but it is technically incorrect. Electron Flow is what actually happens (most of the time). The electrons flow out of the negative side of the battery, through the circuit, and back to the positive side of the battery. Conventional Current Electron Flow

6. Current and Electric Potential • Conventional (positive) current flows from high potential to low potential (high voltage to low voltage) • Electrons flow from low potential to high potential (low voltage to high voltage)

7. How much Current is allowed to flow? • Conductivity (σ) • Resistivity (ρ) • Resistance (R) What do you think these words mean in the context of electrical circuits? Think/Pair/Share

8. Conductivity • Electrical charges can move freely in some materials (conductors) and less freely in other materials (insulators). • How easily charges can move in a material is described, and quantified, by the material’s Conductivity (σ). • Density of free charges • Mobility of free charges

9. Resistivity • A material’s ability to resist the flow of electric charge is known as Resistivity (ρ). ρ=1/σ • Resistivity and Conductivity are inverses of each other (just like f and T) • Units of Resistivity: Ω·m • Resistivity and Conductivity are really material properties. • Resistivity isn’t absolutely constant for a given material. • Typically, Resistivity increases as temperature increases.

10. Resistance • Resistance is an object’s ability to resist the flow of charge, or resist Current through a Circuit. • Resistance depends on both shape and Resistivity. • Resistance, in effect, restricts the area through which charge can flow. R = ρL/A • Units of Resistance are Ohms • The symbol for Resistance is R and the symbol for the units of Resistance is Ω.

11. Resistance in a Circuit Resistor – Something you put in a Circuit to change the Circuit’s Resistance One common type of Resistor is the filament in a light bulb. When current flows into a light bulb, it gets held up in the filament. While it’s hanging out in the filament, it makes the filament extremely hot, and the filament gives off light. Wires are not perfect conductors, but when we analyze circuit problems, we assume zero resistance in the wires.

12. Voltage • Voltage aka Potential Difference aka Electric Potential aka Electrical Potential Difference aka Electric tension aka electric pressure • Voltage is the difference in electric potential energy of a unit charge transported between two points. Voltage is equal to the work done per unit charge against a static electric field to move the charge between two points. • Voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. • Units are Joules/Coulomb or Volts. • http://amasci.com/miscon/voltage.html

13. off on off on Voltage in a Circuit The battery provides voltage that will push current through the bulb when the switch is on. BONUS: How does a battery work?

14. Ohm’s Law • Resistance opposes Current flow • Potential Difference (Voltage) promotes Current flow What is the relationship between R, V, and I?

15. Graphical Relationship • Ohm’s Law isn’t truly a law of physics • Not all materials follow Ohm’s Law • Materials which do are ohmic materials.

16. Ohm’s Law (V=IR) Current in a resistor varies in direct proportion to the voltage applied to it and is inversely proportional to the resistor’s value. Ohm’s Law is the mathematical relationship between current, voltage, and resistance If you know 2 of the 3 quantities, you can solve for the third. V=IR R=V/I I=V/R

17. Example: Ohm’s Law • The flashlight shown uses a 6 volt battery and has a bulb with a resistance of 150 . When the flashlight is on, how much current will be drawn from the battery? V I R Schematic Diagram IR + - VT = VR

18. Electrical Energy and Power Electrical Power is the rate at which Electrical Energy is expended. P = W/t Let’s derive the Electrical Power Equation…hint: W=QV

19. Power • When current flows through a Resistor, electrical energy is being converted into heat energy. • The rate at which this conversion occurs is called the Power dissipated by a resistor. • This Power can be quantified with the following equation: P=IV Units of Power are watts 1 watt is equal to 1 Joule/sec Combine the Power Equation with Ohm’s Law…

20. Circuit Schematics Circuit Schematics are sometimes called Circuit Diagrams • 2-D representation of real circuit elements • Current flow requires a source of potential difference • Battery • Generator • Voltage Source

21. Common Circuit Elements

22. Circuit Configuration Components in a circuit can be connected in one of two ways. Parallel Circuits Both ends of the components are connected together. There are multiple paths for current to flow. Series Circuits • Components are connected end-to-end. • There is only a single path for current to flow. Components (i.e., resistors, batteries, capacitors, etc.)

23. Series Circuits If the path is open anywhere in the circuit, current stops flowing to all components. A circuit that contains only one path for current flow

24. Series Circuits Characteristics of a series circuit • The current flowing through every series component is equal. • The total resistance (RT) is equal to the sum of all of the resistances (i.e., R1 + R2 + R3). The sum of all voltage drops (V1 + V2 + V3) is equal to the total applied voltage (VT). This is called Kirchhoff’s Voltage Law (KVL). VR1 IT + - + + VR2 VT - - - + RT VR3

25. Example: Series Circuit • For the series circuit shown, use the laws of circuit theory to calculate the following: • The total resistance (RT) • The current flowing through each component (IT, I1, I2, & I3) • The voltage across each component (VT, V1, V2, & V3) • Use the results to verify Kirchhoff’s Voltage Law VR1 IT + - IR1 + + VR2 VT IR2 - - IR3 - + RT VR3

26. Parallel Circuits A circuit that contains more than one path for current flow If a component is removed, then it is possible for the current to take another path to reach other components.

27. Parallel Circuits Characteristics of a Parallel Circuit • The voltage across every parallel component is equal. • The total resistance (RT) is equal to the reciprocal of the sum of the reciprocal: • The sum of all of the currents in each branch (IR1 + IR2 + IR3) is equal to the total current (IT). This is called Kirchhoff’s Current Law. IT + + + + VR1 VR2 VR3 VT - - - - RT

28. Example Parallel Circuits • For the parallel circuit shown, use the laws of circuit theory to calculate the following: • The total resistance (RT) • The voltage across each component (VT, V1, V2, & V3) • The current flowing through each component (IT, I1, I2, & I3) • Use the results to verify Kirchhoff’s Current Law IT IR1 IR2 IR3 + + + + VR1 VR2 VR3 VT - - - - 28 RT

29. Combination Circuits Contain both series and parallel arrangements What would happen if you removed light 1? Light 2? Light 3? 1 2 3

30. Kirchoff’s Laws • Kirchoff’s Laws help you solve complicated circuits. • Kirchoff’s Laws say: • At any junction, the current entering equals the current leaving (Junction Rule). • The sum of voltages around a closed loop is 0 (Loop Rule).

31. Steps for using Kirchoff’s Loop Rule • Choose a direction of current, either arbitrarily or based on largest voltage source. Draw arrows on your circuit to indicate this direction. • Follow the loop in the direction you chose. When you cross a resistor, the voltage is –IR, where R is the resistance, and I is the current following through the resistor. This is just an application of Ohm's law. (If you have to follow a loop against the current, though, the voltage across a resistor is written +IR.) • When you cross a battery, if you trace from the – to the + add the voltage of the battery, subtract the battery's voltage if you trace from + to –. • Set the sum of your voltages equal to 0. Solve. If the current you calculate is negative, then the direction you chose was wrong—the current actually flows in the direction opposite to your arrows.

32. The V-I-R Chart -First, enter all the given information into your chart. If resistors haven’t already been given names (like “R1”), you should name them for easy reference. -Next, simplify the circuit to calculate Req, if possible -Once you have two values in a row, you can calculate the third using Ohm’s law. -Remember that if two resistors are in series, the current through one of them equals the current through the other. And if two resistors are in parallel, the voltage across one equals the voltage across the other.

33. RC Circuits: Steady-State Behavior • When you have both Resistors and Capacitors in a circuit, the circuit is called an “RC Circuit”. • A Capacitor’s purpose in a circuit is to store charge. Capacitors are typically charged by batteries. After a capacitor has been connected to a circuit for a time, the capacitor becomes fully charged and prevents the flow of current. This is a situation of “steady-state behavior”.

34. Capacitors in Series • When capacitors occur in series, you add them inversely. The charge stored on each capacitor in series must be the same.

35. Capacitors in Parallel • When capacitors occur in parallel, you add them algebraically. The voltage across each capacitor in parallel must be the same.

36. Capacitance Equations • Charge stored on (or the voltage across) a Capacitor: Q=CV • Energy stored by a Capacitor: PEc=½CV2

37. Extra Notes • “Energy dissipated” = solve for Power, then apply that Power = “Energy dissipated”/time • Terminal Voltage < EMF because of the internal resistance in a battery • VT = EMF - IRB

38. Brightness of a Bulb • The brightness of a bulb depends solely on the Power dissipated by the bulb. • The Resistance of a light bulb is a property of the bulb itself. Therefore, Resistance will not change no matter what the bulb is hooked to.

39. Multimeter An instrument used to measure the properties of an electrical circuit, including Voltage Volts (Voltmeter) Current Amps (Ammeter) Resistance Ohms

40. Voltmeter • Voltmeters are used to measure the potential difference between two points in a circuit. • Voltmeters have very high resistance so as to minimize the current flow through the voltmeter and the voltmeter’s impact on the circuit.

41. Measuring Voltage Set multimeter to the proper V range. Measure across a component, i.e. put the meter in parallel with the resistor. Switch Battery Resistor Light

42. Ammeters • Ammeters are used to measure the Current in a circuit. • Ammeters have very low resistance • Minimizes the potential drop through the ammeter • Minimizes the ammeter’s impact on the circuit

43. Measuring Current Set multimeter to the proper ADC range. Circuit flow must go through the meter. Place meter in series with the component. Switch Battery Resistor Light

44. Ohmmeters • Ohmmeters are used to measure Resistance in a circuit.

45. Measuring Resistance Set multimeter to the proper Ohms range. Measure across the component being tested. Power must be off or removed from the circuit. Switch Battery Resistor Light