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Transcript
Physics 10: Current Electricity A. Circuit Elements (18-1 to 18-5, 19-1) 1. purpose of circuit is to control the direction and amount of charge that flows to circuit elements 2. electric current, I = Q/t (A) a. ampere, A = C/s b. current flows from a high voltage to low voltage 1. Vhigh Vlow (conventional current) 2. analogous to water running down hill c. electron flow through conductor 1. I = Nqe/t a. N is number of electrons b. qe is charge per electron (1.6 x 10-19 C) 2. Vlow Vhigh (opposite conventional current) d. Ohm’s law: V = V = IR (I = V/R)—river analogy 1. electron flow through metal is analogous to water running down a river channel 2. river current depends on channel steepness (steeper channel = faster current): I V 3. river current depends on channel roughness (rougher channel = slower current): I 1/R 4. Ohm's law is a generalization, not natural law 3. electromotive force, emf (E, V or V) a. general term for any devise that can generate a voltage gradient, E = Vhigh – Vlow b. E produced by chemical reaction (battery) or induction (generator) c. terminal voltage (V) and emf (E) of a battery 1. current flow out of a battery is limited by the internal resistance, r, of the battery 2. terminal voltage, V = E ± Ir 3. (–) when discharging, (+) when charging 4. resistor, R () a. ohm, = V/A b. general term for anything that resists current (light bulb, heater, motor) c. R = L/A A L depends on the material and state a. resistivity, (•m) b. increases as temperature increases 2. proportional to length, L (m) 3. inversely proportional to area, A (m2) d. as current flows through a resistor 1. I is constant, I = V/R 2. V decreases, V = -IR 3. power is consumed, P = IV = IV Steps Algebra P = W/t start with substitute QV for W P = (QV)/t P = (Q/t)V regroup P = IV substitute I for Q/t substitute IR for V P = I(IR) = I2R P = (V/R)2R = V2/R substitute V/R for I 5. capacitor (discussed earlier) a. Q = CV measured in Coulombs, C b. C =єoA/d measured in Farads, F (єo = 8.85 x 10-12 C2/N•m2) c. UC = ½QV = ½CV2 = ½Q2/C measured in Joules, J d. E = V/d measured in V/m or N/C 1. Name __________________________ B. 6. symbols for circuit elements 7. Circuit diagram of a battery, resistor, capacitor and switch Series and Parallel Circuit Design (19-2 to 19-5) 1. batteries in series a. total voltage: Es = E1 ± E2 ± E3 b. add when + to – (current exits + pole) c. subtract when + to + (current exits higher V) 2. resistors a. series R1 R2 R3 1. Rs = R1 + R2 + R3 Steps Algebra start with R = Ltot/A substitute L1 + L2 + L3 for Ltot Rs = (L1 + L2 + L3)/A distribute Rs = L1/A + L2/A + L3/A substitute R for L/A Rs = R1 + R2 + R3 2. current, I, is the same for all resistors 3. share of voltage drop, Vn = IRn b. parallel R1 R2 R3 1. 1/Rp = 1/R1 + 1/R2 + 1/R3 Steps Algebra start with R = L/Atot substitute A1 + A2 + A3 for Atot Rp = L/(A1 + A2 + A3) inverse both sides 1/Rp = (A1 + A2 + A3)/L distribute 1/Rp = A1/L + A2/L + A3/L substitute 1/R for A/L 1/Rp = 1/R1 + 1/R2 + 1/R3 2. voltage, V, is the same for all resistors 3. share of current, In = V/Rn 3. capacitors a. series C1 C2 C3 1/Cs = 1/C1 + 1/C2 + 1/C3 Steps Algebra start with C =єoA/dtot substitute d1 + d2 + d3 for dtot Cs = єoA/(d1 + d2 + d3) inverse both sides 1/Cs = (d1 + d2 + d3)/єoA distribute 1/Cs = d1/єoA + d2/єoA + d3/єoA substitute 1/C for d/єoA 1/Cs = 1/C1 + 1/C2 + 1/C3 2. charge, Q, is the same for all capacitors 3. share of voltage drop, Vn = Q/C b. parallel C1 1. C2 1. C3 Cp = C1 + C2 + C3 Steps Algebra start with C =єoAtot/d substitute A1 + A2 + A3 for Atot Cp = єo(A1 + A2 + A3)/d distribute Cp = єoA1/d + єoA2/d + єoA3/d substitute C for єoA/d Cp = C1 + C2 + C3 2. voltage, V, is the same for all capacitors 3. share of charge, Qn = CnV 4. Kirchhoff’s rules a. loop rule: V = 0 for any complete loop b. junction rule: Iin = Iout for any junction 5. Solving complex circuit problems. Determine overall voltage, Etot Etot = 4 V + 6 V = 10 V Determine overall resistance, Rtot 12 1/Rp = 1/R3 + 1/R6 1/Rp = 1/3 + 1/6 = 1/2 3 Rp = 2 4 Rs = Rp + R4 = 2 + 4 = 6 6 1/Rp = 1/Rs + 1/R12 1 1 3 1 5 1/Rp = /6 + /12 = /12 Rp = 4 4 6 Rs = R1 + Rp + R5 V V Rs = 1 + 4 + 5 = 10 Determine current from the battery, I tot = Vtot/Rtot Itot = Vtot/Rtot = 10 V/10 = 1 A Determine voltage loss in resistors in series with the battery, V = ItotR V1 = ItotR1 = (1 A)(1 ) = 1 V V5 = ItotR5 = (1 A)(5 ) = 5 V Determine voltage loss using Kirchhoff's loop rule and/or current through parallel resistors using Kirchhoff's junction rule E6 + E4 + (-V1) + (-V12) + (-V5) = 0 V12 = 4 V I12 = V/R = 4 V/12 = 1/3 A I12 + I4 = 1 A I4 = 2/3 A V4 = R = (2/3 A)(4 ) = 8/3 V (-V4) + (-V3) + V12 = 0 V3 = V6 = 4/3 V I3 = V/R = 4/3 V/3 = 4/9 A 6 + 3 = 2 / 3 A I6 = 2 / 9 A Determine power for all resistors, P = IV Determine voltage across each capacitor (same as voltage across a parallel resistor) For capacitors in series: determine the overall capacitance: 1/Cs = 1/C1 + 1/C2, then calculate the common charge: Qs = CsVtot Determine the charge or voltage (Q = CV) and energy (Uc = ½QV) for all capacitors Experiments 1. Batteries and Bulbs Lab a. Attach wires between one set of battery terminals and one set of light bulb terminals so that the light bulb lights. Diagram the circuit. b. (1) Connect a second light bulb to the circuit using only one additional wire. Diagram the circuit (2) The brightness of the first bulb (increased or decreased). (3) When one light bulb is unscrewed from its socket, the other bulb (stays on or goes out). (4) Why does the other light bulb go out? (This arrangement of light bulbs is called series) c. (1) Connect the two bulbs with the battery using two long and two short wires so that the electricity from the battery can go through one bulb without having to go through the other. Diagram the circuit. (2) The brightness of the bulbs in this arrangement compared to the series circuit arrangement is (brighter or dimmer). (3) When one light bulb is unscrewed from its socket, the other bulb (stays on or goes out). (4) Why does the other light bulb remain lit? (This arrangement of light bulbs is called parallel) d. 2. Series and Parallel Circuit Lab How to use the Multimeter Voltage: Move the red lead to the V/ slot, and then turn the dial to 2-V DC (long line over three dashed lines). Attach the red lead to the resistor/capacitor spring closest to the + pole of the battery and the black lead to the spring on the other side of the resistor/capacitor, then record the measurement. This arrangement is called parallel. If the reading begins with zeros, you can turn the dial to a more sensitive level. Be sure to record the potential with the correct power of 10. Current: Move the red lead to the mA/A slot, and then turn the dial to 1-A DC. Free the resistor wire nearest the + pole of the battery from its spring (leave the other wire in its spring). Attach the red lead to the spring nearest the + pole of the battery. Pinch the black lead and free resistor wire together with your finger and thumb. This arrangement is called series. If the reading begins with zeros, you can turn the dial to a more sensitive level. Be sure to record the current with the correct power of 10. Capacitance: Connect a 100,000- resistor (brownblack-yellow) and capacitor in series (Spring—Resistor— Spring—Capacitor—Spring). Set the multimeter to 2 V DC and connect the meter to the springs on either side of the capacitor (not the resistor). Connect a wire from the (–) terminal of the battery to the capacitor spring farthest from the resistor. When ready to time, connect a wire from the (+) terminal of the battery to the resistor spring farthest from the capacitor. Record the time it takes for the voltage to go from 0.200 V to 1.200 V. Capacitance is proportional to time (Q = It = CV C = (I/V)t = kt). Part 1—Resistors a. Measure the current and voltage for each resistor listed below (each resistors is identified by its color bands). Calculate the resistance. Current Voltage Resistance Color Bands (V) (R = V/I) ( I) Brown-Black-Brown Orange-Orange-Brown Green-Blue-Brown b. (1) Determine the theoretical resistance when the three resistors are attached in series. (1) Connect two batteries and 1 bulb together in a series circuit using two long and one short wire. Diagram the circuit. (2) Place the three resistors in series, measure current and voltage, and then calculate the total resistance. Voltage (V) Resistance (R = V/I) Current (I) (3) Calculate the percent difference between the measured and theoretical values for resistance. c. e. (2) The additional battery makes the bulb (brighter or dimmer). (1) Connect the two batteries and three bulbs so that each bulb shines independently and brightly. Diagram the circuit. (1) Determine the theoretical resistance when the three resistors are attached in parallel. (2) Place the three resistors in parallel, measure current and voltage, and then calculate the total resistance. Voltage (V) Resistance (R = V/I) Current (I) (3) Calculate the percent difference between the measured and theoretical values for resistance. (2) The bulbs are connected in (series or parallel). (3) The batteries are connected in (series or parallel). Part 2—Capacitors a. Follow the instructions above to attach the 100 F capacitor and 100,000 resistor. Record the time it takes to go from 0.200 V to 1.200 V. Repeat with the 330 F capacitor. (Discharge the capacitor by touching a wire between the two sides of the capacitor.) Time, t (s) Capacitance, C (F) Trial 1 Trial 2 Average 100 F b. c. 3. 4. 330 F Calculate k (k = C/t) for each capacitor and the average. 5. (1) Determine the theoretical capacitance when the two capacitors are attached in series. (2) Place the two capacitors in series and measure the time it takes to charge the capacitors. Trial 1 Trial 2 Average 6. 7. 8. (3) Calculate the total capacitance based on the charging time (C = kt), use the average k from (b). 9. (4) Calculate the percent difference between the measured and theoretical values for capacitance. d (1) Determine the theoretical capacitance when the two capacitors are attached in parallel. (2) Place the two capacitors in parallel and measure the time it takes to charge the capacitors. Trial 1 Trial 2 Average (3) Calculate the total capacitance based on the charging time (C = kt), use the average k from (b). (4) Calculate the percent difference between the measured and theoretical values for capacitance. Practice Problems 1. A. Circuit Elements Which is the correct way to light the light bulb with the battery? You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude? (A) Ohm's law is obeyed since the current still increases when V increases (B) Ohm's law is not obeyed (C) This has nothing to do with Ohm's law A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? (A) ¼R (B) ½R (C) 2R (D) 4R When you rotate the knob of a light dimmer, what is being changed in the electric circuit? (A) power (B) current (C) voltage (D) both P and I Two light bulbs operate at 120 V, but one has a power rating of 25 W while the other has a power rating of 100 W. Which one has the greater resistance? (A) 25 W bulb (B) 120 W bulb (C) tie Two space heaters are operated at 120 V. Heater A has twice the resistance as heater B. Which one will give off more heat? (A) A (B) B (C) tie Which current flows from high to low voltage, electron flow or conventional current? How many electrons (qe = -1.60 x 10-19 C) pass when a current of 10 A runs for 25 minutes? 10. What is the current through a 200- resistor if the voltage between its terminals is 15 V? 11. What is the internal resistance of a battery where E = 1.5 V and the terminal voltage = 1.35 V when the current is 3 A? 12. In general, how is resistivity affected by changes in temperature? 13. a. Determine the electrical resistance of tungsten wire ( = 5.0 x 10-8 •m, L = 20 m and A = 1.0 x 10-6 m2). b. Determine the electrical resistance in the same piece of tungsten after it is stretched to a length of 60 m. 14. What is the resistance in a 48-W light that operates at 12 V? 15. What can increase the capacitance for a parallel plate capacitor? 16. A parallel plate capacitor consists of two metal plates separated by 0.006 m and is connected to a 100-V source. The area of each plate is 0.04 m2. Determine the a. capacitance. 2. Two wires, A and B, are made of the same material and have equal lengths, but the resistance of wire A is four times the resistance of wire B. How do their diameters compare? (A) DA = 4DB (B) DA = 2DB (C) DA = ½DB (D) DA = ¼DB b. charge on each plate. c. energy stored. d. electric field. 17. Show how a battery, bulb and two wires must be arranged in order for the bulb to light. Use circuit element symbols. 18. A starter motor draws a current of 50 A through a cable for 5 s. Determine the number of a. coulombs of charge which pass through the cable. b. electrons that pass through the cable. 19. A 50-m long wire with cross section of 3 x 10-6 m2 has a resistance of 0.5 . What is the resistivity? 20. What is the resistance in a light bulb that draws 500 mA current at 3 V. 31. What happens to the total brightness when one light bulb is replaced by a wire? (A) dimmer (B) same (C) brighter (D) no light Questions 32-33 Two light bulbs are parallel with a 12-V battery. 32. What happens to the total brightness when one light bulb is removed? (A) dimmer (B) same (C) brighter (D) no light 33. What happens to the total brightness when one light bulb is replaced by a wire? (A) dimmer (B) same (C) brighter (D) no light Questions 34-36 The three light bulbs have the same resistance. C A B 34. The current through bulb C compared to bulb A is (A) ¼ (B) ½ (C) 2 (D) 4 35. The voltage drop across bulb C compared to bulb A is (A) ¼ (B) ½ (C) 2 (D) 4 36. How much brighter is bulb C compared to A? (A) ¼ (B) ½ (C) 2 (D) 4 Questions 37-39 A 6-A current is measured at point X in a circuit containing identical 1- light bulbs A, B, C, D and E. A C D X B E 37. What is the correct order from greatest (1) to least (5) current? IA 21. A 10- resistor is connected to a 120 V line. Determine a. the current through the resistor. b. the power dissipated in the resistor. 38. 22. What is the power rating of a theater light in which a current of 10 A is caused by 120 V? B. Series and Parallel Circuit Design 23. A 9-V battery is connected to three identical resistors in series. What is the voltage across each resistor? (A) 3 V (B) 9 V (C) 18 V (D) 27 V Questions 24-25 A battery of voltage V is connected to a 4- and 2- resistor in series. 24. What is the same for both resistors? (A) P (B) I (C) V (D) both P and I 25. What is the voltage across the 4- resistor? (A) 1/3V (B) 1/2 V (C) 2/3 V (D) V Questions 26-27 Current, I, enters a parallel circuit containing a 2- resistor and a 4- resistor. 26. What is the same for both resistors? (A) P (B) I (C) V (D) both P and I 27. What is the current through the 4- resistor? (A) 1/3 I (B) ½ I (C) 2/3 I (D) I Questions 28-29 Two light bulbs (resistors) are in series, with a wire and switch connected parallel to one of the bulbs. Compared to when the switch is open, how does the bulb's brightness change when the switch is closed? 39. 40. 41. 42. 43. Total R Total I Total P V for 3 A B 28. Bulb A? (A) dimmer (B) same (C) brighter (D) no light 29. Bulb B? (A) dimmer (B) same (C) brighter (D) no light Questions 30-31 Two light bulbs are in series with a 12-V battery. 30. What happens to the total brightness when one light bulb is removed? (A) dimmer (B) same (C) brighter (D) no light IB IC ID IE (A) 1 1 3 3 3 (B) 2 2 4 4 1 (C) 4 4 2 2 1 (D) 2 2 1 1 4 Which generates the most light? (A) A + B (B) C + D (C) E Which has the smallest voltage drop? (A) A (B) C (C) E Two capacitors are in series with a 12-V battery. What happens to the total capacitance when one capacitor is replaced by a wire? (A) decrease (B) same (C) increase Two capacitors are in parallel a 12-V battery. What happens to the total capacitance when one capacitor is replaced by a wire? (A) decrease (B) same (C) increase Highlight the correct option for the following sentences. a. (Current or Voltage) is the same for resistor in series. b. (Current or Voltage) is the same for resistors in parallel. c. You can disconnect one device without stopping the current in a (series or parallel) circuit. d. Two light bulbs arranged in (series or parallel) will generate the most light. 3- and 6- resistors in series connected to 6 V. V for 6 P for 3 P for 6 44. 3- and 6- resistors in parallel connected to 6 V. 48. 3-F and 6-F capacitors in parallel connected to 6 V. Total R Ctot Total I Qtot Total P UC-tot I for 3 Q3 I for 6 Q6 P for 3 UC-3 P for 6 UC-6 45. Given R1 = 6 , R2 = 12 , and R3 = 2 are arranged in the following circuit. Determine the R1 R3 R2 12 V 49. Three capacitors, C1 = 10 F, C2 = 20 F, C3 = 30 F, are arranged as shown below. Determine the C1 C3 120 V C2 a. total resistance. a. total capacitance. b. total current leaving the battery. b. total charge stored on C3. c. voltage drop across R3. c. voltage across C3. d. voltage, current and power for each resistor. V P I d. voltage, charge and potential energy for each capacitor. V Q UC R1 C1 R2 C2 R3 C3 e. Show that the power dissipated in the resistors equals the power generated by the battery? 50. Show where a voltmeter (V) and ammeter (A) would be placed in order to measure volts and amps in the resistor. (A/V) 46. Highlight the correct option for the following sentences. a. Capacitor (Charge or Voltage) is the same in series. b. Capacitor (Charge or Voltage) is the same in parallel. 47. 3-F and 6-F capacitors in series connected to 6 V. (A/V) 51. Three 12-resistors can be connected in four different ways. Determine overall resistance of each combination? Ctot Qtot UC-tot 52. Determine the equivalent resistance when three resistors rated at 2-, 4-, and 6- are connected in V3 series V6 parallel UC-3 UC-6 53. A 100-W, 120-V lamp bulb is connected in parallel with a 60-W, 120-V lamp bulb. What is their combined resistance? 54. Consider the following circuit. 5 6 90V 1 Determine the a. 4. Two 4.0- resistors are connected to a I6-V battery. 12 Rtot The power generated in the circuit is (A) 8 W (B) 16 W (C) 32 W Itot (D) 64 W b. Determine current, voltage and power for each resistor. V P Resistor I Questions 5-6 relate to the four incomplete circuits below composed of resistors R, all of equal resistance, and capacitors C, all of equal capacitance. A battery that can be used to complete any of the circuits is available. R R C R (A) (B) 1 5 12 6 d . 55. Consider the following circuit ⁄switch 15 C (C) R 50V a. b. 6F d . (D) R R R 10 5. Into which circuit should the battery be connected to obtain the greatest steady power dissipation? (2) energy stored in the 6 F capacitor. 6. Which circuit will retain stored energy if the battery is connected to it and then disconnected? When the switch is closed, determine (1) Voltage across the capacitor. 7. A battery with an internal resistance of 4 connected to a l6- and a 20- resistor in series. The current in the 20- resistor is 0.3 A. When the switch is open, determine (1) charge on the 6 F capacitor. (2) charge on the 6 F capacitor. (3) energy stored in the 6 F capacitor. Practice Multiple Choice Briefly explain why the answer is correct in the space provided. Questions 1-2 The four resistors have the lengths, L, and cross-sectional areas, A, indicated and are made of material with the same resistivity. (A) L = 1 m, A = 1 m2 (B) L = 2 m, A = 1 m2 (C) L = 1 m, A = 2 m2 (D) L = 2 m, A = 2 m2 1. Which resistor has the least resistance? 2. Which has the greatest resistance? 3. A circuit consists of a 10- resistor, a 15- resistor, and a 20- resistor connected in parallel across a 9-V battery. What is the equivalent resistance of this circuit? (A) 0.2 (B) 2 (C) 4.6 (D) 45 What is the emf, E, of the battery? (A) 1.2 V (B) 6.0 V (C) 10.8 V 8. (D) 12 V A lamp, a voltmeter V, an ammeter A, and a battery with zero internal resistance are connected as shown. How would the addition of a second lamp affect the ammeter and voltmeter readings? A V A V (A) increase same (B) decrease decrease (C) same increase (D) decrease decrease 9. An electric circuit contains a variable resistor connected to a battery. Which graph best represents the relationship between current and resistance in this circuit? (A) (B) (C) (D) 17. What is the equivalent resistance of this circuit? (A) 72 (B) 3 (C) 18 (D) 0.33 18. How much power is dissipated in the 36- resistor? (A) 110 W (B) 3 W (C) 48 W (D) 4 W 19. What is the voltage between points X and Y? Questions 10-12 refer to the circuit shown below. 10. The equivalent capacitance for this network is (A) 10/7 F (B) 3/2 F (C) 7/3 F (D) 7 F (A) 1 V (B) 2 V (C) 3 V (D) 4 V (C) 5 (D) 20 20. What is the value of r? 11. The charge stored in the 5-F capacitor is (A) 360 C (B) 500 C (C) 710 C (D) 1,100 C 12. The electrical energy stored in the 5-F capacitor is (A) 0.025 J (B) 0.050 J (C) 2.5 J (D) 500 J (A) 0 (B) 1 Questions 13-14 refer to partial electric circuit. Questions 21-22 refer to the circuit shown below. 13. The electrical resistance between point X and point Y is (A) 4/3 (B) 2 (C) 11/4 (D) 4 14. The current is (A) the same everywhere in the circuit (B) greater at point X than at point Y (C) greater in the 1 resistor than in the 2 resistor (D) greater in the 2 resistor than in the 3 resistor 15. A 10- heater is used to heat water. If the heater draws 3 A for 100 s, how much energy is transferred to the water? (A) 30 (B) 300 (C) 3,000 (D) 9,000 Questions 16-18 The circuit consisting of four resistors and a 12-V battery. 16. What is the current measured by the ammeter? (A) 0.5 A (B) 2 A (C) 72 A (D) 4 A 21. What is the current I1? (A) 0.8 mA (B) 1.0 mA (C) 2.0 mA (D) 3.0 mA 22. How do the currents I1, I2, and I3 compare? (A) I1 > I2 > I3 (B) I1 > I3 > I2 (C) I2 > I1 > I3 (D) I3 > I1 > I2 23. What percentage of the power generated by a 0.5 A, 120 V electric motor is used to lift a 9 kg mass against gravity at an average velocity of 0.5 m/s? (A) 7% (B) 13% (C) 25% (D) 75% 24. A wire of length L and radius r has a resistance R. What is the resistance of a second wire made from the same material that has a length ½L and a radius ½r? (A) 4R (B) 2R (C) R (D) ½R Practice Free Response 1. Consider the following circuit. C1 C2 R3 R4 R2 R1 R5 9V a. R6 C3 Determine the following values. R3 + R4 R3-4 + R5 Rtot Itot V5 I5 I3 C1 + C2 Q1+2 V1 V2 Q3 b. Complete the table for each resistor and capacitor. R V P Resistor I Overall ___ R1 1 R2 3 R3 3 R4 3 R5 3 R6 3 Capacitor C C1 30 F C2 15 F C3 20 F Q V Uc