Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Circuits containing multiple elements Series and parallel combinations Complex Multi-loop Circuits RC circuits Chapter 23 Circuits Topics: Sample question: An electric eel can develop a potential difference of over 600 V. How do the cells of the electric eel’s body generate such a large potential difference? Slide 23-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. RC Circuits RC circuits are circuits containing resistors and capacitors. In RC circuits, the current varies with time. The values of the resistance and the capacitance in an RC circuit determine the time it takes the capacitor to charge or discharge.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. RC Circuits The current and the capacitor voltage decay to zero after the switch closes, but not linearly.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. RC Circuits The decays of the voltage and the current are exponential decays:

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. RC Circuits

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. QuickCheck The following circuits contain capacitors that are charged to 5.0 V. All of the switches are closed at the same time. After 1 second has passed, which capacitor is charged to the highest voltage?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. QuickCheck Which capacitor discharges more quickly after the switch is closed? A. Capacitor A B. Capacitor B C. They discharge at the same rate. D. We can’t say without knowing the initial amount of charge.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Charging a Capacitor In a circuit that charges a capacitor, once the switch is closed, the potential difference of the battery causes a current in the circuit, and the capacitor begins to charge. As the capacitor charges, it develops a potential difference that opposes the current, so the current decreases, and so does the rate of charging. The capacitor charges until ΔV C = ℇ.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Charging a Capacitor The equations that describe the capacitor voltage and the current as a function of time are

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide Tau = RC

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitor behavior while charging Before Switch is thrown After Capacitor is charged

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 2.In the circuit shown below, the switch is initially closed and the bulb glows brightly. When the switch is opened, what happens to the brightness of the bulb? A.The brightness of the bulb is not affected. B.The bulb gets dimmer. C.The bulb gets brighter. D.The bulb initially brightens, then dims. E.The bulb initially dims, then brightens. Slide Additional Clicker Questions

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 2.In the circuit shown below, the switch is initially closed and the bulb glows brightly. When the switch is opened, what happens to the brightness of the bulb? B.The bulb gets dimmer. Slide Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. QuickCheck The red curve shows how the capacitor charges after the switch is closed at t = 0. Which curve shows the capacitor charging if the value of the resistor is reduced? B

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. QuickCheck The red curve shows how the capacitor charges after the switch is closed at t = 0. Which curve shows the capacitor charging if the value of the resistor is reduced? Smaller time constant. Same ultimate amount of charge. B

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nuclear Decay and Half-Lives If you start with N 0 unstable nuclei, after an interval of time called the half-life, you’ll have ½ N 0 nuclei remaining. The half-life t 1/2 is the average time required for one-half the nuclei to decay. The number of nuclei N remaining at time t is No matter how many nuclei there are at any point in time, the number decays by half during the next half-life.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nuclear Decay and Half- Lives The figure shows the decay of a sample of radioactive nuclei.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nuclear Decay and Half-Lives The number of radioactive atoms decreases exponentially with time.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. QuickCheck A sealed box is completely evacuated (perfect vacuum), then 1,000,000 radioactive atoms are added. Their half- life is 2 days. After 4 days have passed, how many atoms are in the box? A. 1,000,000 B. 500,000 C. 250,000 D. 0

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nuclear Decay and Half-Lives The decay of radioactive nuclei is an exponential decay. The equation for the number of atoms after a half-life can be written in terms of a time constant τ that is related to the half-life:

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Magnets and the magnetic field Electric currents create magnetic fields Magnetic fields of wires, loops, and solenoids Magnetic forces on charges and currents Magnets and magnetic materials Chapter 24 Magnetic Fields and Forces Topics: Sample question: This image of a patient’s knee was made with magnetic fields, not x rays. How can we use magnetic fields to visualize the inside of the body? Slide 24-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 3-D Arrows, Cross Products, and Right Hand Rule 1 Slide 24-2 Showing vectors in 3D Cross Product For direction use Right-hand rule 1 Right-hand rule 1 (RHR 1) => for finding direction of cross-product vector (Cross-Product Rule) 1.Point right hand in the direction of the first vector (vector A) 2.Rotate your right hand until you can point your fingers in the direction of the second vector (vector B) 3.Thumb points in direction the cross-product vector (vector C)

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric vs. Magnetic Interactions 1.Nature of Magnetic Interactions Slide 24-2

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Discovering Magnetism Slide 24-6

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field Slide 24-7

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Mapping Out the Field of a Bar Magnet Slide 24-8

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Mapping Out the Magnetic Field Using Iron Filings Slide 24-9

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Drawing Field Lines of a Bar Magnet Slide 24-10

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Magnetic Fields Produced by Bar Magnets A single bar magnet (closeup) Slide 24-11

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Magnetic Fields Produced by Bar Magnets Two bar magnets, unlike poles facing Two bar magnets, like poles facing Slide 24-12

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Slide 24-13

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Magnetic Fields from Two Magnets Bar Magnets A and B are placed at right angles. Two compasses, X and Y are placed so that they are equidistant from the two magnets as shown A.) The arrow in compass X indicates the direction in which the North pole of the compass is pointing. Indicate the North and South ends of both magnets in the diagram B.) Draw an arrow in compass Y to show the direction in which the North pole of the compass needle would point. Slide 24-2

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Magnetic Fields Around Us Slide 24-14

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Key Points Three types of magnetic interactions 1.no interaction with either pole of a magnet => object is non-magnetic 2.attracted to both poles of a magnet => object is magnetic 3.Attracted to one pole and repelled by the other pole => object is a magnet Magnetic field vector from a bar magnet is a super position of the magnetic field vectors from the N and S poles: Vector from N pole points away from N pole Vector from S pole points towards S pole Field lines form complete loops inside and outside of magnet Field lines outside magnet go from N to S poles Field lines inside magnet go from S to N poles Magnetic Field vectors at a point are tangential to Magnetic Field Lines

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Currents Also Create Magnetic Fields A long, straight wire A current loopA solenoid Slide 24-15

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field of a Straight Current-Carrying Wire Slide 24-16

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-17

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Representing Vectors and Currents That Are Perpendicular to the Page Slide 24-18

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P? Slide 24-19

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P? Slide 24-20

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Drawing Field Vectors and Field Lines of a Current-Carrying Wire Slide 24-21

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Drawing a Current Loop Slide 24-22

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field of a Current Loop Slide 24-23

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field of a Solenoid A short solenoidA long solenoid Slide 24-24

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnitude of the Field due to a Long, Straight, Current-Carrying Wire Slide 24-25

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 24-26

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding A.10 A to the right. B.5 A to the right. C.2.5 A to the right. D.10 A to the left. E.5 A to the left. F.2.5 A to the left. The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire? Slide 24-27

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E.5 A to the left. The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire? Slide Answer