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### bt401p

1. 1. ELECTRIC CURRENT A flow of charge from one place to another. The unit is Ampere , which equal to a flow of 1 coulomb per second.
2. 2. Moving charges as a current <ul><li>Its described as a stream of moving charges. </li></ul><ul><li>May range very small currents such as the nerve impulses to a large as the solar wind emitted by the sun. </li></ul><ul><li>There must be a “net” flow of charges towards one direction. </li></ul>
3. 3. When moving charges is not a current <ul><li>When there is no net flow of charge even though there are actual movement. </li></ul><ul><li>Example: </li></ul><ul><ul><li>Electrons of a copper conductor in absence of electric potential. </li></ul></ul><ul><ul><li>Electrons just move randomly the charge flowing charge flowing to one direction is equal to those flowing to the other direction. </li></ul></ul>
4. 4. Electric current in a conductor <ul><li>An isolated conductor in absence of electric potential contains free flowing electrons but no electric current. </li></ul>Isolated conductor charges
5. 5. continuation: <ul><li>A conductor connected to a dry cell or battery has the necessary electric potential to influence the flow of charges towards one direction, hence producing current. </li></ul>Battery + - Conductor Charges Direction of charges
6. 6. continuation: <ul><li>Electric current ( I ) is defined as the amount of charges passing through a hypothetical plane intersecting the conductor per unit of time. </li></ul><ul><li>Its unit is coulomb per second (C/s), also called ampere (A). </li></ul><ul><li>Where: </li></ul><ul><ul><li>I = Current (ampere, A) </li></ul></ul><ul><ul><li>Q = Charge (coulomb, c) </li></ul></ul><ul><ul><li>t = Time (second, s) </li></ul></ul>
7. 7. continuation: - - - - - - t = t 0 t = t 0 + 1 s plane plane
8. 8. continuation: <ul><li>Independent to the selection of hypothetical plane </li></ul>a b c a’ b’ c’ I I
9. 9. Sample problem: <ul><li>A wire carries a current of 0.8 ampere. How many electrons passes every section of the wire every one second? </li></ul>
10. 10. Current is a scalar quantity <ul><li>Electric current is moving along a conductor has only two possible directions. </li></ul><ul><li>Electric current are scalars. Adding and Subtracting the current does not consider the orientation of the conductor in space. </li></ul>
11. 11. continuation: I 0 I 1 I 2 I 0 = I 1 + I 2
12. 12. DIRECTION OF CURRENT <ul><li>In reality, electric current are movement of electrons along the conductor. </li></ul><ul><li>For historical reason, current is treated as flow of positive charges to the direction opposite that of the actual movement of electrons. </li></ul>
13. 13. continuation: <ul><li>These positive charges are not actual particles. They are called holes , vacant spaces where there should be an electron. The charge of a hole is +1.6 x 10 -19 C . </li></ul><ul><li>Electrons are known as negative charge carriers . Holes are known as positive charge carriers . </li></ul>
14. 14. Drift Speed <ul><li>The net motion of charged particles as a group: </li></ul>Where: I = electric current (A) n = charge concentration v d = drift velocity (m/s) e = charge of electron A = cross-sectional area of conductor(m 2 ) <ul><li>Usually very small (10 -5 or 10 -4 m/s) compared to random motion of charges (10 6 m/s) </li></ul>I in I in A
15. 15. Current Density <ul><li>Current per unit of cross-sectional area of a conductor. </li></ul><ul><li>A vector quantity with the same direction as the motion of positive charge carriers. </li></ul>Where: I = electric current (A) J = current density (A/m 2 ) n = charge concentration v d = drift velocity (m/s) e = charge of electron A = cross-sectional area of conductor(m 2 )
16. 16. Sample Problem: <ul><li>A 491 gauge copper wire has a nominal diameter of 0.64 mm. This wire carries a constant current of 1.67 A to a 4,910 watts lamp. The density of free electron is 8.5 x 10 28 electrons/m 3 . Find the current density and the magnitude of drift velocity. </li></ul>
17. 17. Types of Current <ul><li>Direct current </li></ul><ul><ul><li>The direction of current is constant. </li></ul></ul><ul><ul><li>The graph of current vs time is a straight line. </li></ul></ul><ul><ul><li>Developed by Tomas Alva Edison </li></ul></ul><ul><ul><ul><li>Soon replaced by alternating current as primary means of transmitting electricity, but still used in battery operated devices. </li></ul></ul></ul>
18. 18. continuation: <ul><li>Alternating Current </li></ul><ul><ul><li>The direction and magnitude of the current continuously changes between two extremes. </li></ul></ul><ul><ul><li>The graph of current vs time is sinosoid. </li></ul></ul><ul><ul><li>Developed by Nikola Tesla and George Westinghouse , forming rivalry with Thomas Edison on War of the Currents . </li></ul></ul><ul><ul><li>The most commonly used method of electric transmission today. </li></ul></ul>
19. 19. Types of Current <ul><li>Direct Current </li></ul>Alternating Current I (A) t (s) I (A) t (s)
20. 20. ELECTRIC RESISTANCE
21. 21. Electric Resistance <ul><li>Property of the conducting medium that weakens the transmission of electric current. </li></ul><ul><li>Denoted as R and its unit is Ohm ( Ω ) . </li></ul>Where: R = Resistance (Ohm, Ω ) ρ = resistivity ( Ω m) L = Length of the wire (m) A = cross-sectional area of a wire(m 2 )
22. 22. Sample Problem: <ul><li>A piece of 1.0 m wire has a resistance of 0.19 ohms. Calculate the resistivity of the wire. The cross-sectional area of the wire is 0.5 mm 2 . </li></ul>ρ L A
23. 23. Resistivity & Conductivity <ul><li>Resistivity ( ρ ) </li></ul><ul><ul><li>Measure of how much resistance a material possesses against electric current. </li></ul></ul><ul><ul><li>Intrinsic property of a material that depends on its electronic structure. </li></ul></ul>Conducting material Electric field
24. 24. continuation: <ul><li>Measure by placing the material between two plates with constant electric field ( E ) and taking the ratio of electric field and current density ( J ) . </li></ul><ul><li>Varies with temperature </li></ul>Where: ρ = resistivity ( Ω m) E = electric field (N/c) J = current density (A/m 2 )
25. 25. <ul><li>Conductivity </li></ul><ul><ul><li>Measure of how the material is capable of conducting electricity. </li></ul></ul><ul><ul><li>Reciprocal of resistivity. </li></ul></ul>continuation:
26. 26. Variation of Resistivity with Temperature <ul><li>Over a wide range of temperature, the graph of resistivity vs temperature of metal is linear. </li></ul>400 200 0 1200 1400 2 8 0 4 6 10 600 800 1000 Resistivity 10 -8 Ω m Room temperature Temperature (Kelvin)
27. 27. Variation of Resistivity with Temperature <ul><li>Thus it can be represented by a Linear equation. </li></ul>Where: ρ = resistivity ( Ω m) ρ 0 = resistivity at room temperature ( Ω m) T = temperature (Kelvin,K) T 0 = room temperature (K) α = coefficient of resistivity (K -1 )
28. 28. continuation: <ul><li>The Temperature coefficient of resistivity ( α ) determines how much resistivity increases with temperature. </li></ul><ul><li>Its unit is (per Kelvin)K -1 . </li></ul>
29. 29. Sample Problem: <ul><li>What is the resistivity of iron at 200K? Use the values of resistivity (at room temperature) and temperature coefficient of the resistivity in the handout. </li></ul>
30. 30. Ohm’s Law <ul><li>The current I (Ampere, A) is directly proportional to the potential difference V (Volt,V) with resistance R (ohms, Ω ) as the proportionality constant. </li></ul>
31. 31. continuation: <ul><li>Assumed that the resistance does not vary with voltage or current. </li></ul><ul><li>Not all conducting material follow “Ohm’s Law”. Those are follow are said to be ohmic , while those that do not are said to be non ohmic . </li></ul>
32. 32. Current Potential Difference graph of a 1000 W resistor , an Ohmic device. -4 -2 0 +2 +4 -2 +2 0 Current (mA) Potential Difference (V)
33. 33. Current vs Potential Difference graph of a pn junction diode , a non-ohmic device. -4 -2 0 +2 +4 -2 +2 0 Current (mA) Potential Difference (V)
34. 34. Single Loop Circuit <ul><li>Circuit </li></ul><ul><ul><li>Close network of electronic devices through which current constantly flows. </li></ul></ul>EMF Device Maintain potential difference. Provides steady flow of charge. EMF stand for Electromotive force . R EMF I + - + - I
35. 35. The Resistor <ul><li>Provides a resistance to the circuit. </li></ul><ul><li>It was specially designed to only provide certain amount of resistance. </li></ul><ul><li>An Ohmic device </li></ul><ul><ul><li>Such conductor device. </li></ul></ul><ul><ul><li>It was verified experimentally by the German physicist Georg Ohm (1787-1854). </li></ul></ul>
36. 36. Electromotive Force <ul><li>A circuit consists of electrons from the negative terminal of a battery to the positive terminal of the battery. </li></ul><ul><li>Electrons must then return to the negative terminal, or current will stop flowing. </li></ul><ul><li>The electron are forced into this higher potential by a electromotive force. </li></ul>EMF
37. 37. continuation: <ul><li>EMF Devices: </li></ul><ul><ul><ul><li>Battery or Dry Cell </li></ul></ul></ul><ul><ul><ul><li>Electrochemical Cell </li></ul></ul></ul><ul><ul><ul><li>Electric Generator </li></ul></ul></ul><ul><ul><ul><li>Photovoltaic Cell </li></ul></ul></ul>
38. 38. <ul><li>Internal Resistance </li></ul><ul><ul><li>The resistance found inside real batteries </li></ul></ul><ul><ul><li>Lessen the output voltage of the battery. </li></ul></ul><ul><ul><li>Denoted as r i </li></ul></ul><ul><ul><li>Its SI unit is Ohms (Ω) . </li></ul></ul><ul><ul><li>A real battery is now drawn as: </li></ul></ul>continuation: EMF r i
39. 39. continuation: <ul><li>Terminal Potential Difference ( TPD ) </li></ul><ul><li>The output voltage of a source of emf after internal resistance takes effect. </li></ul><ul><li>The equation used to solve for terminal potential difference is: </li></ul><ul><li>TPD = E – Ir i </li></ul><ul><li>Where: </li></ul><ul><ul><li>TPD = voltage across the source (V) </li></ul></ul><ul><ul><li>E = voltage if the source is ideal emf (V) </li></ul></ul><ul><ul><li>r i = internal resistance of the source (Ω) </li></ul></ul><ul><ul><li>I = current flowing through the battery (A) </li></ul></ul>
40. 40. Sample Problem: <ul><li>A 6.0 V battery is connected to an external 6.0 0hms resistor. </li></ul><ul><ul><li>What is the value of the current flowing through the external circuit if there is no internal resistance, </li></ul></ul><ul><ul><li>What is the value of the current flowing through the external circuit when the internal resistance is 0.3 ohms? </li></ul></ul>
41. 41. Resistors in Single Loop Circuit
42. 42. <ul><ul><li>Where: R is resistance, I is electric current and V is electric potential difference. </li></ul></ul>Resistors in Series Circuit. R 3 V T I T + - + R 2 + R 1 + - - - R T
43. 43. Equivalent resistance in a Series Circuit
44. 44. Sample problem: <ul><li>Resistors R 1 = 2.00 ohms, R 2 = 3.00 ohms and R 3 = 4.00 ohms are in series connection with a voltage source of 100.0 volts. Find the equivalent resistance, electric current and electric potential difference. </li></ul>
45. 45. <ul><li>Resistor in Parallel Circuit </li></ul>R 3 V T I T + - + R 2 + R 1 + - - - R T I 3 I 2 I 1
46. 46. Equivalent resistance in a Parallel Circuit
47. 47. Sample problem: <ul><li>Resistors R 1 = 3.00 ohms, R 2 = 5.00 ohms and R 3 = 7.00 ohms are in parallel connection with a voltage source of 110.0 volts. Find the equivalent resistance, electric current and electric potential difference. </li></ul>
48. 48. Resistors in Single Loop Circuit <ul><li>Resistor in Series-Parallel Circuit </li></ul>R 3 V T I T + - + R 2 + R 1 + - - - R T
49. 49. POWER IN CIRCUITS
50. 50. The Power in the Circuits <ul><li>Flow of current across a circuit. </li></ul>
51. 51. continuation: <ul><li>Movement of a charge across a electric device: </li></ul><ul><ul><li>It moves from higher potential to lower potential. </li></ul></ul><ul><ul><ul><li>Hence, there is a decrease in potential energy. </li></ul></ul></ul>Q
52. 52. continuation: <ul><li>If there is a decrease in potential energy, there must be a transmission to another form of energy. </li></ul><ul><ul><ul><li>Light bulb: to heat and light. </li></ul></ul></ul><ul><ul><ul><li>Electric motor: to mechanical energy </li></ul></ul></ul><ul><ul><ul><li>Resistor: Internal energy/heat. </li></ul></ul></ul>
53. 53. continuation: <ul><li>The rate at which electric potential energy is transformed to another form of energy is the POWER in the circuit. </li></ul>
54. 54. Sample Problem: <ul><li>A current flowing through a 25.0 ohm resistor is 2.0 A. How much power is dissipated by the resistor. </li></ul>
55. 55. MULTILOOP CIRCUIT <ul><li>Provides multiple paths for current. </li></ul><ul><li>When one component was cut-off, others can still function. </li></ul>
56. 56. What happen when one component in a series circuit was cut-off?
57. 57. What happen when one component in a multiloop circuit was cut-off?
58. 58. continuation: <ul><li>Current in a Multiloop Circuit </li></ul><ul><ul><li>The point where three or more segments of the conductor meet is called the junction. </li></ul></ul><ul><ul><li>The current split at the junction. </li></ul></ul>Junction current
59. 59. GUSTAV KIRCHHOFF <ul><li>German physicist who, in the collaboration with Robert William Bunsen, develop ed the science of spectrum analysis. </li></ul><ul><li>He showed that each element, when heated to incandescence. </li></ul><ul><li>He produced a characteristic pattern of emission lines. </li></ul><ul><li>He formulated Kirchhoff’s Law for electric circuit. </li></ul><ul><li>(1824-1887) </li></ul>
60. 60. <ul><li>In any closed circuit, the algebraic sum of all EMF’s and potential drop is equal to zero. (Using loop direction) </li></ul>KIRCHHOFF’S LAW R 2 + Emf 1 + - R 1 + Emf 2 + - R 3 + Loop 1 Loop 2 I 1 I 2 I 3 -
61. 61. <ul><li>At any point in a circuit, the sum of the currents leaving the junction point is equal to the sum of all the current entering the junction point. (Using current direction). </li></ul>KIRCHHOFF’S LAW R 2 + ε 1 + - R 1 + ε 2 + - R 3 Junction point I 1 I 3 I 2 +
62. 62. Sample Problem: <ul><li>In a given circuit below, Find: a) I 1 , b) I 2 and c) I 3 </li></ul>10 Ω + 9v + - 15 Ω + 12v + - 5 Ω I 1 I 3 I 2 +
63. 63. RC CIRCUIT (Resistor and Capacitor in a circuit)
64. 64. <ul><li>Resistor- Capacitor in a circuit. </li></ul>R + - C S 1 S 2 ε + - Where: ε = Batteries (Emf) S 1 & S 2 = Switches R = Resistor C = Capacitor Open Close
65. 65. Charging a capacitor R + - C S 1 S 2 ε + - I I I I I closed open Where: V R = Potential difference across the resistor. V C = Potential difference across the capacitor. I
66. 66. continuation <ul><li>Current I O at the moment S 1 closed ( t = 0) </li></ul><ul><li>Current I at any time t after S 1 closed: </li></ul><ul><li>After some time t </li></ul><ul><ul><li>The charge of the capacitor (q) increases </li></ul></ul><ul><ul><li>Current ( I ) decreases. </li></ul></ul>
67. 67. continuation <ul><li>Until the capacitor reaches its equilibrium charge (q eq ), happen when V C reaches V C = ε , which result to I = 0 </li></ul>
68. 68. continuation <ul><li>Charge and current of the capacitor at any given time t after t = 0. </li></ul>
69. 69. <ul><li>The time constant ( τ ) of RC series circuit. </li></ul><ul><li>The unit of time constant is second. </li></ul><ul><li>At time t = τ </li></ul><ul><ul><li>Q = 0.63 C ε </li></ul></ul><ul><ul><li>I = 0.37 I o </li></ul></ul><ul><li>The charging time of RC circuits are often stated in terms of time constant. </li></ul>continuation
70. 70. Sample Problem: <ul><li>A resistor with resistance R=1.0 x 10 6 Ω , capacitor with capacitance C=2.2 x 10 -6 F, a voltage source with ε = 100 v, and a switch are all connected in a single loop series circuit. The switch is initially open. When the switch is closed, calculate: </li></ul><ul><ul><ul><ul><li>Initial current across the resistor </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Equilibrium charge of the capacitor </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Time constant of the circuit </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Current through the resistor after 5 seconds </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Charge of the capacitor after 5 second </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Charge of the capacitor at t = τ </li></ul></ul></ul></ul>