Physics 1302W Introductory Physics for Science and Engineering II Clem Pryke, Associate Professor. Lecture 23
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1 Physics 1302W Introductory Physics for Science and Engineering II Clem Pryke, Associate Professor Lecture 23
2 Quiz 2 Score Distribution
3 This Week Chapter 31 homework will be set in MasteringPhysics by midnight tonight due one week later. You will receive quiz and formal writeup #1 papers back in discussion tomorrow. The quiz grades will be posted on dept. website shortly thereafter. Formal lab writeup #2 due by 5pm Friday Read chapter 27 for next week.
4 Today s Lecture Ø RC Circuits: Resistors and Capacitors Ø Charging and discharging capacitors Ø Parallel and series capacitors in circuits
5 Recap: RC Circuits When the capacitor has a different potential difference than the battery the resistor will have a potential difference across its terminals current (ΔV=IR) When the capacitor has a the same potential difference as the battery the resistor will have zero potential difference across its terminals no current (ΔV=IR)
6 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge?
7 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? Do the circuit analysis: Assume capacitor has a potential V V 0 (it s charging)
8 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? Do the circuit analysis: Assume capacitor has a potential V V 0 (it s charging) Identify current Positive charge flows to left side of capacitor to raise potential up: Draw clockwise current I
9 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? Do the circuit analysis: Work through the closed loop (in direction of I) V a-b + V b-c + V c-a = 0
10 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? Positive because left side at higher potential than right side Charging to match battery V 0 Do the circuit analysis: Work through the closed loop (in direction of I) V a-b + V b-c + V c-a = 0 V + V b-c + V c-a = 0
11 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? Do the circuit analysis: Work through the closed loop (in direction of I) V a-b + V b-c + V c-a = 0 V + V b-c + V c-a = 0 V V 0 + V c-a = 0
12 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? Do the circuit analysis: Work through the closed loop (in direction of I) V a-b + V b-c + V c-a = 0 V + V b-c + V c-a = 0 V V 0 + V c-a = 0 V V 0 + IR = 0
13 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have: V V 0 + IR = 0 We are interested in the charge Q on the capacitor Replace variables with charge Q
14 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have: V V 0 + IR = 0 For a capacitor
15 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have: V V 0 + IR = 0 For a capacitor
16 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have:
17 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have: Current is the rate charge flows into capacitor
18 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have: Current is the rate charge flows into capacitor
19 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have:
20 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? So we have: Rearrange terms: You learn how to solve these equations like this one in a differential equations course
21 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? We have: The solution is: Verify by inserting solution into differential equation
22 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? We have: The solution is: Left Side: Verify by inserting solution into differential equation
23 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? We have: The solution is: Left Side: Verify by inserting solution into differential equation
24 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? We have: The solution is: Left Side: Verify by inserting solution into differential equation
25 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? We have: The solution is: Left Side: Verify by inserting solution into differential equation Right Side:
26 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? We have: The solution is: Left Side: Verify by inserting solution into differential equation Right Side:
27 Charging a capacitor in a RC circuit The resistor causes it to take longer to charge the capacitor How long does it take to build up charge? We have: The solution is: Left Side: Verify by inserting solution into differential equation Right Side:
28 Charging a capacitor in a RC circuit
29 Charging a capacitor in a RC circuit
30 Charging a capacitor in a RC circuit
31 Charging a capacitor in a RC circuit
32 Charging a capacitor in a RC circuit
33 Discharging a capacitor in a RC circuit If a capacitor is charged and you connect a resistor across it, the capacitor will discharge From Ohm s Law IR = V
34 Discharging a capacitor in a RC circuit If a capacitor is charged and you connect a resistor across it, the capacitor will discharge From Ohm s Law IR = V From capacitance formula IR = Q/C V = Q/C
35 Discharging a capacitor in a RC circuit If a capacitor is charged and you connect a resistor across it, the capacitor will discharge From Ohm s Law IR = V From capacitance formula IR = Q/C V = Q/C Insert Negative because current created by removing charge Q from capacitor
36 Discharging a capacitor in a RC circuit If a capacitor is charged and you connect a resistor across it, the capacitor will discharge From Ohm s Law IR = V From capacitance formula IR = Q/C V = Q/C Insert
37 Discharging a capacitor in a RC circuit If a capacitor is charged and you connect a resistor across it, the capacitor will discharge From Ohm s Law IR = V From capacitance formula IR = Q/C V = Q/C Insert Solution is:
38 Discharging a capacitor in a RC circuit
39 Discharging a capacitor in a RC circuit
40 Discharging a capacitor in a RC circuit Discharging Losing charge
41 Charging and Discharging Charging Capacitor Discharging Capacitor
42 Capacitor/Bulb Demo A battery is connected through a push switch to a large capacitor with the return path through a lamp. When the switch closes the circuit current flows to charge the capacitor. The lamp lights brightly and then dims exponentially. Connecting the lamp directly across the capacitor it becomes the power source current flows to discharge the capacitor through the lamp which again initially glows brightly and then dims exponentially. 42
43 RC Circuit Driven with Square Wave Input Demo In this demo the power supply is periodically switched on and off. When it is on the capacitor charges and the voltage across it ramps up exponentially. When it off the capacitor discharges and the voltage ramps back down again exponentially. By adjusting the R and C values the time constant of exponential changes. 43
44 Example: Lifetime Capacitor Battery Some emergency hand cranked flashlights use capacitors to store charge Capacitors can be charged and discharged unlimited times You can have the flashlight sitting on a shelf for 20 years, crank it up, and it will work! Even rechargeable batteries have a shelf life and eventually can t be recharged (bad for storing for an emergency)
45 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
46 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
47 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
48 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
49 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
50 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
51 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
52 Example: Lifetime Capacitor Battery Suppose you can charge the capacitor up to 5V The capacitor completes a circuit with a 25Ω light bulb. The bulb is on as long as there at least 1V across it What is the minimum capacitance of the capacitor for the bulb to stay on for 5 minutes (300 s)?
53 Clicker Question
54 Clicker Question
55 Clicker Question
56 Clicker Question
57 Clicker Question Part 2
58 Clicker Question Part 2
59 Clicker Question Part 2
60 Capacitors in Parallel What happens when you put 2 capacitors in parallel
61 Capacitors in Parallel What happens when you put 2 capacitors in parallel The capacitors act like one device that stores a charge Q 1 +Q 2 for a voltage V
62 Capacitors in Parallel What happens when you put 2 capacitors in parallel
63 Capacitors in Parallel What happens when you put 2 capacitors in parallel
64 Capacitors in Parallel What happens when you put 2 capacitors in parallel
65 Capacitors in Parallel What happens when you put 2 capacitors in parallel Parallel caps act like one cap with the sum of capacitance
66 Capacitors in Series What happens when you put 2 capacitors in series +Q Q +Q Q C 1 C 2 Because of the conservation of charge the same charge must be on both capacitors since the charge moves between plates V
67 Capacitors in Series What happens when you put 2 capacitors in series +Q Q C S The capacitors act like one device that stores a charge Q for a voltage V V S
68 Capacitors in Series What happens when you put 2 capacitors in series +Q Q V = V 1 + V 2 C S The capacitors act like one device that stores a charge Q for a voltage V V S
69 Capacitors in Series What happens when you put 2 capacitors in series +Q Q V = V 1 + V 2 C S The capacitors act like one device that stores a charge Q for a voltage V V S
70 Capacitors in Series What happens when you put 2 capacitors in series +Q Q V = V 1 + V 2 C S The capacitors act like one device that stores a charge Q for a voltage V V S
71 Capacitors in Series What happens when you put 2 capacitors in series +Q Q V = V 1 + V 2 C S The capacitors act like one device that stores a charge Q for a voltage V V S
72 Capacitors in Series What happens when you put 2 capacitors in series +Q Q V = V 1 + V 2 C S The capacitors act like one device that stores a charge Q for a voltage V V S
73 Capacitors in Series What happens when you put 2 capacitors in series +Q Q V = V 1 + V 2 C S V S Series caps act like one cap Capacitance found by summing inverses
= (0.400 A) (4.80 V) = 1.92 W = (0.400 A) (7.20 V) = 2.88 W
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