2. Electric Circuits AP Physics 1 Conroe High School

3. A Basic Circuit All electric circuits have three main parts 1.A source of energy 2.A closed path 3.A device which uses the energy If ANY part of the circuit is open the device will not work!

4. Electricity can be symbolic of Fluids Circuits are very similar to water flowing through a pipe A pump basically works on TWO IMPORTANT PRINCIPLES concerning its flow There is a PRESSURE DIFFERENCE where the flow begins and ends A certain AMOUNT of flow passes each SECOND. A circuit basically works on TWO IMPORTANT PRINCIPLES There is a "POTENTIAL DIFFERENCE aka VOLTAGE" from where the charge begins to where it ends The AMOUNT of CHARGE that flows PER SECOND is called CURRENT.

5. Quantity Symbol Unit Unit Symbol VoltageCurrentResistancePower V I RP VoltAmpereOhmsWatts VA Ω W Electricians are a little like plumbers of electrons We can often think about water flowing to help us visualize how electrons flow

6. Voltage The force that pushes electrons through a wire P.d. potential difference- like voltage. we will use them interchangeably

7. Potential Difference =Voltage=EMF In a battery, a series of chemical reactions occur in which electrons are transferred from one terminal to another. There is a potential difference (voltage) between these poles. The maximum potential difference a power source can have is called the electromotive force or (EMF), . The term isn't actually a force, simply the amount of energy per charge (J/C or V)

8. ELECTROMOTIVE FORCE A source of electromotive force (emf) is a device that converts, chemical, mechanical, or other forms of energy into the electric energy necessary to maintain a continuous flow of electric charge. The source of the emf in this case is chemical energy.

9. Current The flow of electrons. This is actually the amount of electrons that move past a point on a conductor in a given amount of time. Rivers and streams have different currents (rates of flow) so it is w/ wires

10. Current Current is defined as the rate at which charge flows through a surface. The current is in the same direction as the flow of positive charge (for this course) Note: The “I” stands for intensity

11. There are 2 types of Current DC = Direct Current - current flows in one direction Example: Battery AC = Alternating Current- current reverses direction many times per second. This suggests that AC devices turn OFF and ON. Example: Wall outlet (progress energy)

12. ELECTRIC CURRENT The electric current I is the rate of flow of charge Q past a given point on an electric conductor. Units: C/s = Ampere (A)

13. The direction of conventional current is always the same as the direction in which positive charges would move, even if the actual current consists of a flow of electrons. In a wire, electrons are the only charged particles moving in an electrical current.

14. Resistance the opposition to the flow of current in a conductor In very loose terms, its like friction for electrons Certain factors effect resistance in a wire

15. Resistance Resistance (R) – is defined as the restriction of electron flow. It is due to interactions that occur at the atomic scale. For example, as electron move through a conductor they are attracted to the protons on the nucleus of the conductor itself. This attraction doesn’t stop the electrons, just slow them down a bit and cause the system to waste energy. The unit for resistance is the OHM, 

16. More ResistanceLess Resistance length Cross sectional area Material Temp Cu Al coldhot Resistance can be used to control current in a circuit. They can also do work

17. RESISTIVITY The resistance of a wire of uniform cross-sectional area is determined by: The kind of material The length The cross-sectional area The temperature Where ρ is the resistivity of the material in Ω.m, l is the length in m, and A is the cross-sectional area in m 2.

18. 12.3 What is the resistance of a 20 m length of copper wire with a diameter of 0.8 mm? ρ = 1.72x10 -8 Ω.m l = 20 m r = d/2 = 4x10 -4 m A = πr 2 = π(4x10 -4 ) 2 = 5.02x10 -7 m 2 = 0.685 Ω

19. OHM’S LAW "For a given resistor at a particular temperature, the current is directly proportional to the applied voltage." Units: V/A = ohm (Ω)

20. 12.1 The voltage between the terminals of an electric heater is 80 V when there is a current of 6 A in the heater. What is the current if the voltage is increased to 120 V? V 1 = 80 V I = 6 A V 2 = 120 V = 13.3 Ω = 9 A

21. Ohm’s Law “The voltage (potential difference, emf) is directly related to the current, when the resistance is constant” Since R=  V/I, the resistance is the SLOPE of a  V vs. I graph R= resistance = slope

22. Four devices are commonly used in the laboratory to study Ohm’s law: the battery, the voltmeter, the ammeter and a resistance. The ammeter and voltmeter measure current and voltage respectively. Ammeter measures current through the battery, the filament, and itself. This arrangement measures the voltage across the battery.

23. The Voltmeter and Ammeter The voltmeter and ammeter cannot be just placed anywhere in the circuit. They must be used according to their DEFINITION. Since a voltmeter measures voltage or POTENTIAL DIFFERENCE it must be placed ACROSS the device you want to measure. That way you can measure the CHANGE on either side of the device. Voltmeter is drawn ACROSS the resistor Since the ammeter measures the current or FLOW it must be placed in such a way as the charges go THROUGH the device. Current goes THROUGH the ammeter

24. The following symbols are used in electric circuits:

25. 12.2 A current of 6A flows through a resistance of 300 Ω for 1 hour. a. What is the power loss? I = 6 A R = 300 Ω t = 1 hour P = I 2 R = (6) 2 (300) = 10,800 W b. How much heat is generated in loss? Q = Pt = 10800 (1)(3600) = 3.89x10 7 J

26. POWER It is interesting to see how certain electrical variables can be used to get POWER. Let’s take Voltage and Current for example.

27. Other useful power formulas These formulas can also be used! They are simply derivations of the POWER formula with different versions of Ohm's law substituted in.

29. ELECTRIC POWER AND HEAT LOSS The rate at which heat is dissipated in an electric circuit is referred to as the power loss. P = V I =I 2 R = Units: watts (W) P = I 2 R P = V I

36. In conclusion, there are two requirements which must be met in order to establish an electric circuit. The requirements are: 1.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 creating an electric potential difference across the two ends of the external circuit. 2.There must be a closed conducting loop in the external circuit which stretches from the high potential, positive terminal to the low potential negative terminal.

37. Simple Circuit When you are drawing a circuit it may be a wise thing to start by drawing the battery first, then follow along the loop (closed) starting with positive and drawing what you see.

39. RESISTORS IN SERIES - In a series circuit, the current is the same at all points along the wire. I T = I 1 = I 2 = I 3 - An equivalent resistance is the resistance of a single resistor that could replace all the resistors in a circuit. The single resistor would have the same current through it as the resistors it replaced. R E = R 1 + R 2 + R 3 - In a series circuit, the sum of the voltage drops equal the voltage drop across the entire circuit. V T = V 1 + V 2 + V 3

42. RESISTORS IN SERIES

44. 12.4 Two resistances of 2 Ω and 4 Ω respectively are connected in series. If the source of emf maintains a constant potential difference of 12 V. a. Draw a schematic diagram with an ammeter and a voltmeter.

45. 12.4 Two resistances of 2 Ω and 4 Ω respectively are connected in series. If the source of emf maintains a constant potential difference of 12 V. b. What is the current delivered to the external circuit? R e = R 1 + R 2 = 2 + 4 = 6 Ω = 2 A c. What is the potential drop across each resistor? V 1 = I R 1 = 2(2) = 4 V V 2 = I R 2 = 2(4) = 8 V

48. Example A series circuit is shown to the left. a)What is the total resistance? b)What is the total current? c)What is the current across EACH resistor? d)What is the voltage drop across each resistor?( Apply Ohm's law to each resistor separately) R(series) = 1 + 2 + 3 = 6   V=IR 12=I(6) I = 2A They EACH get 2 amps! V 1   2 VV 3  =(2)(3)= 6VV 2  =(2)(2)= 4V Notice that the individual VOLTAGE DROPS add up to the TOTAL!!

49. PARALLEL CIRCUITS - In a parallel circuit, each resistor provides a new path for electrons to flow. The total current is the sum of the currents through each resistor. I T = I 1 + I 2 + I 3 - The equivalent resistance of a parallel circuit decreases as each new resistor is added. - The voltage drop across each branch is equal to the voltage of the source. V T = V 1 = V 2 = V 3

52. RESISTORS IN PARALLEL

53. Example To the left is an example of a parallel circuit. a) What is the total resistance? b) What is the total current? c) What is the voltage across EACH resistor? d) What is the current drop across each resistor? (Apply Ohm's law to each resistor separately) 2.20  3.64 A 8 V each! 1.6 A 1.14 A 0.90 A Notice that the individual currents ADD to the total.

56. Compound (Complex) Circuits Many times you will have series and parallel in the SAME circuit. Solve this type of circuit from the inside out. WHAT IS THE TOTAL RESISTANCE?

60. Compound (Complex) Circuits Suppose the potential difference (voltage) is equal to 120V. What is the total current? 1.06 A What is the VOLTAGE DROP across the 80  resistor? 84.8 V

61. Compound (Complex) Circuits What is the VOLTAGE DROP across the 100  and 50  resistor? 35.2 V Each! What is the current across the 100  and 50  resistor? 0.352 A 0.704 A Add to 1.06 A

62. Find the total resistance and the total current for this circuit. V 1 = 120V R 1 = 20  R 2 = 20  R 3 = 20  R 4 = 10  R 5 = 10 

65. KIRCHHOFF’S LAWS An electrical network is a complex circuit consisting of current loops. Kirchhoff developed a method to solve this problems using two laws. Law 1. The sum of the currents entering a junction is equal to the sum of the currents leaving that junction. This law is a statement of charge conservation.

66. A junction (j) refers to any point in the circuit where two or three wires come together. j

67. KIRCHHOFF’S LAWS Law 2. The sum of the emfs around any closed current loop is equal to the sum of all the IR drops around that loop. (Ohm’s Law: V = IR) This law is a statement of energy conservation.

68. Gustav Robert Kirchhoff (1824-1887)

69. 12.5 The total applied voltage to the circuit in the figure is 12 V and the resistances R 1, R 2 and R 3 are 4, 3 and 6 Ω respectively. a. Determine the equivalent resistance of the circuit. R 2 and R 3 are in parallel (R P ) R p = 2 Ω R P and R 1 are in series R e = 4 + 2 = 6 Ω

70. b. What is the current through each resistor? = 2 A I 1 = 2 A (series) V 1 = I 1 R 1 = 2(4) = 8 V The voltage across the parallel combination is therefore: 12 - 8 = 4 V each = 1.33 A = 0.67 A

71. 12.6 Find the equivalent resistance of the circuit shown. 1 and 2 are in series: 1+ 2 = 3 Ω this combination is in parallel with 6: this combination is in series with 3: 2 + 3 = 5 Ω this combination is in parallel with 4: R P = 2.22 Ω = R eq R P = 2 Ω

72. 12.7 A potential difference of 12 V is applied to the circuit in the figure below. a. Find the current through the entire circuit R 1 and R 2 are in parallel: R P = 2 Ω This combination is in series with R 3 : 2 + 4 = 6 Ω This combination is now in parallel with R 4 : = 3 Ω = R eq

73. = 4 A I T = I 3 + I 4 = 2 A I 3 = I T - I 4 = 4 - 2 = 2 A b. Find the current through each resistor.

74. The voltage for the parallel combination is: V' = V - I 3 R 3 = 12 - (2)(4) = 4 V = 1 AI 2 = 2 - 1 = 1 A

75. Which schematic has the largest total resistance?

76. What is the total resistance in the circuit? What current does the battery provide?

77. Which graph best displays the relationship between power and voltage? P=V 2 /R

78. How come many people get shocked by house current but they aren’t burned badly? How come others are killed? Dry Skin is very high in resistance[100,000  ], wet skin is much lower in resistance [1,000  ]. Figure out the current that flows when your skin is dry and the voltage is 110V Figure out the current that flows when your skin is wet and the voltage is 110V

79. EMF AND TERMINAL POTENTIAL DIFFERENCE Every source of emf ( Є ) has an inherent resistance called internal resistance represented by the symbol r. This resistance is a small resistance in series with the source of emf. The actual terminal voltage V T across a source of emf with an internal resistance is given by: V T = Є - I rUnits: Volts (V)

80. 12.8 A load resistance of 8 Ω is connected to a battery whose internal resistance is 0.2 Ω a. If the emf of the battery is 12 V, what current is delivered to the load? Є = 12 V R L = 8 Ω r = 0.2 Ω = 1.46 A b. What is the terminal voltage of the battery? V T = Є - I r = 12 - 1.46(0.2) = 11.7 V

81. 12.9 a. Determine the total current delivered by the source of emf to the circuit in the figure. V = 24 V. The resistances are 6, 3, 1, 2 and 0.4 Ω respectively. this combination is in series with R 3 : 2 + 1 = 3 Ω R 1 and R 2 are in parallel: this combination is now in parallel with R 4 : R P = 1.2 Ω R P = 2 Ω

82. finally the internal resistance r is in series giving the equivalent resistance: R eq = 1.2 + 0.4 = 1.6 Ω = 15 A

83. b. What is the current through each resistor? V T = Є - I r = 24 - 15(0.4) = 18 V V 4 = V T = 18 V = 9 A I 3 = I T - I 4 = 15 - 9 = 6 A V 3 = I 3 R 3 = 6(1) = 6 V V 1 = V 2 = 18 - 6 = 12 V each = 2 A = 4 A

84. Ammeter Voltmeter Rheostat Source of EMF Rheostat A Ammeters and Voltmeters V Emf - +

85. Galvanometer 0 10 20 10 20 NS The galvanometer uses torque created by small currents as a means to indicate electric current. A current I g causes the needle to deflect left or right. Its resistance is R g.. The sensitivity is determined by the current required for deflection.

86. Operation of an Ammeter The galvanometer is often the working element of both ammeters and voltmeters. A shunt resistance in parallel with the galvanometer allows most of the current I to bypass the meter. The whole device must be connected in series with the main circuit. I = I s + I g RgRgRgRgI RsRsRsRs IsIsIsIs IgIgIgIg The current I g is negligible and only enough to operate the galvanometer. [ I s >> I g ]

87. Operation of an Voltmeter The voltmeter must be connected in parallel and must have high resistance so as not to disturb the main circuit. A multiplier resistance R m is added in series with the galvanometer so that very little current is drawn from the main circuit. V B = I g R g + I g R m RgRgRgRgI VBVBVBVB IgIgIgIg The voltage rule gives: RmRmRmRm

88. CAPACITORS IN SERIES AND PARALLEL These are the symbols used in different arrangements of capacitors:

89. CAPACITORS IN SERIES

90.  Series capacitors always have the same charge.  The voltage across the equivalent capacitor C eq is the sum of the voltage across both capacitors.

91. CAPACITORS IN PARALLEL

92.  Parallel Capacitors always have the same voltage drop across each of them.  The charge on the equivalent capacitor C eq is the sum of the charges on both capacitors.

93. 19.9 a. Find the equivalent capacitance of the circuit. C 2 and C 4 are in series = 1.33 μF C 2 = 2 μF, C 3 = 3 μF, C 4 = 4 μF V = 120 V C 3 is now in parallel with C 2,4 C eq = C 3 + C 2,4 = 3 +1.33 = 4.33 μF

94. b. Determine the charge on each capacitor. The total charge of the system Q T = C eq V = 4.33 (120) = 520 μC Q 3 = C 3 V = 3(120) = 360 μC Q 2 and Q 4 have the same charge since they are in series: Q 2 = Q 4 = Q T - Q 3 = 520 - 360 = 160 μC Q 3 = 360 μC, Q 2 = Q 4 =160 μC

95. c. What is the voltage across the 4 μF capacitor? = 40 V The remaining voltage (120 - 40 = 80 V) goes through the C 2 capacitor.

96. RC CIRCUITS A resistance-capacitance (RC) circuit is simply a circuit containing a battery, a resistor, and a capacitor in series with one another. An RC circuit can store charge, and release it at a later time. A couple of rules dealing with capacitors in an RC circuit: 1. An empty capacitor does not resist the flow of current, and thus acts like a wire. 2. A capacitor that is full of charge will not allow current to flow, and thus acts like a broken wire.

97. When the switch is closed, the capacitor will begin to charge. RC Circuits

98. If an isolated charged capacitor is connected across a resistor, it discharges: RC Circuits

99. 19.10 Three identical resistors, each with resistance R, and a capacitor of 1.0 x 10 ‑ 9 F are connected to a 30 V battery with negligible internal resistance, as shown in the circuit diagram above. Switches S I and S 2 are initially closed, and switch S 3 is initially open. A voltmeter is connected as shown.

100. a. Determine the reading on the voltmeter.

102. b. Switches S l and S 2 are now opened, and then switch S 3 is closed. Determine the charge Q on the capacitor after S 3 has been closed for a very long time.

103. After the capacitor is fully charged, switches S 1 and S 2 remain open, switch S 3 remains closed, the plates are held fixed, and a conducting copper block is inserted midway between the plates, as shown below. The plates of the capacitor are separated by a distance of 1.0 mm, and the copper block has a thickness of 0.5 mm.

104. c. i. What is the potential difference between the plates?

105. ii. What is the electric field inside the copper block?

106. iii. On the diagram, draw arrows to clearly indicate the direction of the electric field between the plates.

107. iv. Determine the magnitude of the electric field in each of the spaces between the plates and the copper block.