Welcome back to PHY101: Major Concepts in Physics I Photo: J. M. Schwarz
Announcements In class today we will finish Chapter 18 on circuits and begin Chapter 19 (sections 1 and 8) on magnetic fields. There is a lab on circuits this week. Please attend. Stay tuned for next week s lab on the direct current (DC) motor. HW 9 on Chapters 18 and 19 is due on Friday, November 16, at 5PM in your TA s mailbox. Don t forget about the Physics Clinic in PB112, which is open from 9-9 Monday-Thursday and 9-5 Friday.
Eighth set of Three Big Questions What is electric potential energy and electric potential? How does one store/harness the electric potential energy? How do electrical circuits work? 3
Eighth set of Three Big Questions What is electric potential energy and electric potential? How does one store/harness the electric potential energy? How do electrical circuits work? 4
Definition of current: The SI unit of current, equal to one coulomb per second, is the ampere (A). Slide 5
The electrical resistance R is defined to be the ratio of the potential difference (or voltage ) Δ V across a conductor to the current I through the material: Definition of resistance: In SI units, electrical resistance is measured in ohms (symbol Ω, the Greek capital omega), defined as Slide 6
Resistance depends on size and shape. We expect a long wire to have higher resistance than a short one (everything else being the same) and a thicker wire to have a lower resistance than a thin one. The electrical resistance of a conductor of length L and cross-sectional area A can be written: The equation assumes a uniform distribution of current across the cross section of the conductor. Slide 7
Two rules, developed by Gustav Kirchhoff (1824 1887), are essential in circuit analysis. Kirchhoff s junction rule states that the sum of the currents that flow into a junction - any electric connection - must equal the sum of the currents that flow out of the same junction. The junction rule is a consequence of the law of conservation of charge. Since charge does not continually build up at a junction, the net rate of flow of charge into the junction must be zero. Slide 8
Kirchhoff s loop rule is an expression of energy conservation applied to changes in potential in a circuit. Recall that the electric potential must have a unique value at any point; the potential at a point cannot depend on the path one takes to arrive at that point. Therefore, if a closed path is followed in a circuit, beginning and ending at the same point, the algebraic sum of the potential changes must be zero. Slide 9
Kirchhoff s Loop Rule For any path in a circuit that starts and ends at the same point. (Potential rises are positive; potential drops are negative.) Slide 10
When a current flows down a metal wire A. electrons are moving in the direction of the current. B. electrons are moving opposite the direction of the current. C. protons are moving in the direction of the current. D. protons are moving opposite the direction of the current.
If a 22 Ohm resistor has a current of 2.0 A flowing through it, what is the potential difference across it? A. 0.091 V B. 44 V C. 11 V D. 24 V
Wire A carries 4 A into a junction, wire B carries 5 A into the same junction, and another wire is connected to the junction. What is the current in this last wire? A. 4 A away from the junction B. 9 A into the junction C. 9 A away from the junction D. 4 A into the junction
Resistors in Series When one or more electric devices are wired so that the same current flows through each one, the devices are said to be wired in series. Slide 15
Resistors in Series The circuit shows two resistors in series. The straight lines represent wires, which we assume to have negligible resistance. Negligible resistance means negligible Voltage drop ( V = IR ), so points connected by wires of negligible resistance are at the same potential. The junction rule, applied to any of the points A D, tells us that the same current flows through the emf and the two resistors. Slide 16
Resistors in Series Let s apply the loop rule to a clockwise loop DABCD. From D to A we move from the negative terminal to the positive terminal of the emf, so ΔV = + 1.5 V. Since we move around the loop with the current, the potential drops as we move across each resistor. Slide 17
Resistors in Series Slide 18
For any number N of resistors connected in series, Note that the equivalent resistance for two or more resistors in series is larger than any of the resistances. Slide 19
Resistors in Parallel When one or more electrical devices are wired so that the potential difference across them is the same, the devices are said to be wired in parallel. Slide 20
Resistors in Parallel In the figure, an emf is connected to three resistors in parallel with each other. The left side of each resistor is at the same potential since they are all connected by wires of negligible resistance. Likewise, the right side of each resistor is at the same potential. Thus, there is a common potential difference across the three resistors. Slide 21
Resistors in Parallel Applying the junction rule to point A yields How much of the current I from the emf flows through each resistor? The current divides such that the potential difference V A V B must be the same along each of the three paths and it must equal the emf E. From the definition of resistance, Slide 22
Resistors in Parallel Therefore, the currents are Slide 23
Resistors in Parallel The three parallel resistors can be replaced by a single equivalent resistor R eq. In order for the same current to flow, R eq must be chosen so that E = IR eq. Then I/E = 1/R eq and Slide 24
For N resistors connected in parallel, Note that the equivalent resistance for two or more resistors in parallel is smaller than any of the resistances (1/ R eq > 1/ R i, so R eq < R i ). Note also that the equivalent resistance for resistors in parallel is found in the same way as the equivalent capacitance for capacitors in series. Slide 25
Four 12 Ohm resistors are connected together. What is the least resistance that can be attained with these resistors? A. 12 Ohm B. 6.0 Ohm C. 3.0 Ohm D. 2.0 Ohm
18.6 Example problem: (a) Find the equivalent resistance for the two resistors in the figure if R 1 = 20.0 Ω and R 2 = 40.0 Ω. (b) What is the ratio of the current through R 1 to the current through R 2? Slide 27
18.6 Strategy Points A and B are at the same potential; points C and D are at the same potential. Therefore, the voltage drops across the two resistors are equal; the two resistors are in parallel. The ratio of the currents can be found by equating the potential differences in the two branches in terms of the current and resistance. Slide 28
Solution (a) 18.6 (b) Slide 29
Another example problem: (a) Find the equivalent resistance between points A and B for the combination of resistors shown. (b) An 18 V emf is connected to the terminals A and B. What is the current through the 1.0 Ω resistor connected directly to point A?
How about adding capacitors in series and in parallel?
How does one compute the power in any element of a circuit?
Ninth set of Three Big Questions What are magnetic fields? How can we harness magnetic fields to do work? How do magnetic fields affect the motion of certain objects? 35
Permanent Magnets A bar magnet is one instance of a magnetic dipole. By dipole we mean two opposite poles. Slide 36
Permanent Magnets Like poles repel one another and opposite poles attract one another. The magnetic field is represented by the symbol. Slide 37
Do non-permanent magnets exist?
The Oersted Effect demo!
Magnetic Field due to Current in a Long Straight Wire Slide 40
To Find the Direction of the Magnetic Field due to a Long Straight Wire 1. Point the thumb of the right hand in the direction of the current in the wire. 2. Curl the fingers inward toward the palm; the direction that the fingers curl is the direction of the magnetic field lines around the wire. 3. As always, the magnetic field at any point is tangent to a field line through that point. For a long straight wire, the magnetic field is tangent to a circular field line and, therefore, perpendicular to a radial line from the wire. Slide 41
Magnetic field due to a long straight wire: where I is the current in the wire and µ 0 is a universal constant known as the permeability of free space. The permeability plays a role in magnetism similar to the role of the permittivity (ϵ 0 ) in electricity. Slide 42
In SI units, the value of µ 0 is The constant µ 0 can be assigned an exact value because the magnetic forces on two parallel wires are used to define the ampere, which is an SI base unit. Slide 43
What does the magnetic field generated by a solenoid look like? First of all, what is a solenoid?
What does the magnetic field generated by a solenoid look like? First of all, what is a solenoid? Let s do a demo!
Magnetic Field due to a Solenoid Slide 46
If a long solenoid has N turns of wire and length L, then the magnetic field strength inside is given by: Magnetic field strength inside an ideal solenoid: In the equation, I is the current in the wire and n = N/L is the number of turns per unit length. Note that the field does not depend on the radius of the solenoid. Slide 47
Application: Magnetic Resonance Imaging Slide 48
A bar magnet has a north pole and a south pole. This arrangement is referred to as a A. monopole. B. equipole. C. bipole. D. dipole.
Example problem: Estimate the magnetic field a distances of 1 micron, 1 mm, and 1 m produced by a current of 3 microamps along the nerve of the human arm. Model the nerve as a straight current-carrying wire. Compare your results with the magnetic field of the Earth near the surface.
Lab 8 and the DC motor