# University Physics 227N/232N Current and Ohm s Law, Resistors, Circuits, and Kirchoff Lab this Friday, Feb 28 So NO QUIZ this Friday!

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1 University Physics 227N/232N Current and Ohm s Law, Resistors, Circuits, and Kirchoff Lab this Friday, Feb 28 So NO QUIZ this Friday! Dr. Todd Satogata (ODU/Jefferson Lab) and Fred Miller Monday, February Happy Birthday to Floyd Mayweather Jr, Bronson Arroyo, Mitch Hedberg, Steve Jobs, and Brian Schmidt (yes, 2011 Nobel Prize) Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 1

2 Review: Capacitors A capacitor is a pair of conductors, insulated from each other, and used to store charge and energy. The two conductors are given equal but opposite charges Definition of capacitance: C Q/ Q = C Capacitance is a physical property of the capacitor. A parallel plate capacitor has two parallel conductors of equal area A separated by distance d, possibly a dielectric C parallel plate = apple A 4 kd = applec 0 C 0 = A 4 kd The dielectric constant κ for a vacuum is 1 apple >= 1 ±Q Energy stored in a capacitor U stored in capacitor = 1 2 C 2 = 1 2 Q = 1 2 Q 2 C Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 2

3 Review: Connecting Capacitors in Parallel We usually just write the voltage difference as even though it s a difference! Here the capacitors have the same potential difference. C 1 = Q 1 C 2 = Q 2 Q = Q 1 + Q 2 C = C 1 + C 2 Equivalent capacitance C C = Q Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 3

4 Same charges ±Q on middle (overall neutral) conductor Review: Connecting Capacitors in Series Here the capacitors have the same charge Q. 1 C 1 C 1 = Q 1 1 = Q C 1 2 C 2 C 2 = Q 2 2 = Q C 2 = C = 1 C C 2 Equivalent capacitance C C = Q = Q C Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 4

5 Circuits with Parallel and Series Capacitors To analyze a circuit with several capacitors, look for series and parallel combinations. Calculate the equivalent capacitances, and redraw the circuit in simpler form. This technique will work later for more general electric circuits. You got to practice this in your homework and on last week s quiz. Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 5

6 Chapter 24: Current, Resistors, and Ohm s Law Classical analog electronic circuits are made from four types of elements Capacitors Electrical energy storage: springs Resistors Electrical energy dissipation: friction oltage sources (EMF) Electrical energy (potential difference) sources Conductive wires Treated as perfectly conductive (But we know they really have some small resistance too) We characterize electrical circuits with oltage (potential) differences between various points Current (electron or charge) flow I between various points DC: Constant current (including zero) AC: time-varying current Charges on capacitors Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 6 R C - +

7 What is Electric Current? Electric current relates to the net flow of electric charge Now we can talk about how charges move in our conductors that aren t quite ideal (they take time to move) How many charges pass a certain point in a certain amount of time? At a given time I dq dt Ampere Coulomb sec dq is really counting charge: + are positive, - are negative Current has a direction and doesn t require a conductor to exist Although conductors are materials that allow electrons to move a lot more easily than in most other materials I = dq dt Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 7

8 Electric Current in Wires We ll be considering electric current I in conductive wires for now Remember, current is a flow of charges Net charge doesn t build up on wires or other electric circuit elements Even on capacitors! They have +/-Q on plates and stays net neutral But the charges of the plates +/-Q do change as current moves charges onto them So current I is the same along a single piece of wire I I I I What about wire junctions? There charges go one way or another, or come from one way or another So the total of current pointing in equals the total of current point out I 1 I 2 I 2 I 1 I 1 = I 2 + I 3 I 3 I 3 I 1 + I 2 + I 3 =0 Negative current is really just current that s really opposite to your arrow Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 8

9 Multi-Step Problems The homework had you do a few problems that are multi-step You have to use multiple applications of the same equations and principles to untangle voltages, capacitances, charges of all elements within a circuit We ll do even more of this as we add in more circuit elements Important principles that generally hold true Elements that are in parallel have the same voltage They share the same conductors on both sides But they can (and often do) have different current I 1 I = I 1 + I 2 Elements that are in series have the same current Or, for capacitors, the same charge But they can (and often do) have different voltages I I Applying these can already get you far! = Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 9 I

10 Although it can be a fair amount of work Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 10

11 Conduction of Current in Metal Wires A metal contains a sea or gas of free electrons: They re confined to the metal (conductor) but not bound to individual atoms. The electrons move about in random directions with high thermal velocities. On average, there s no current associated with thermal motion. Applying an electric field adds a small drift velocity on the electrons motion. All electrons share the drift velocity, so it results in a current. Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 11

12 Ohm s Law (Microscopic) Electrons often collide with ions (nuclei) in the metal s crystal structure They usually lose energy this way This limits how easily the electrons flow through the material This produces resistance to current flow Quantified as conductivity of the metal It s defined by how the current density is related to the electric field ~J ~E J E Resistivity: 1 Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 12

13 Ohm s Law for Macroscopic Resistive Devices How do we relate this to electric current and voltage? : potential difference ~E : Electric field ~J : Current density I : Electric current We can calculate a total resistance to current flowing based on the resistivity ρ and physical properties of the object R = L A 10 cm long, 1mm 2 Cu wire: R =1.7m A general rule (called a law though it s really not truly a law): = IR Ohm s Law R = I 1Ohm=1 Amp olt e.g. this law tends to fall apart for very low and very high temperatures Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 13

14 Resistors and a Quick Calculation Macroscopic objects with electric resistance are another basic building block of electric circuits These are resistors We assume they have a lot more resistance than the (generally conductive) wires that connect them A modest conductive wire as a resistance of mω Electrical resistors have resistances of Ω to kω to MΩ = 15 R = 30 = IR I = dq/dt A 30 Ω resistor has a voltage of 15 between its sides What is the current in the resistor? How much charge flows through the resistor in 1 second? Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 14

15 Power Dissipated in a Resistor We had a formula for the energy stored in a capacitor U stored in capacitor = 1 2 C 2 = 1 2 Q = 1 2 Q 2 C C Q This is the energy stored in a capacitor at a particular charge Now we re considering circuits where charges is moving I = dq dt The power P (energy per unit time!) dissipated by a resistive device with resistance R is P = I = I 2 R = 2 R = IR Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 15

16 Circuits, Symbols, and EMF Electric circuits are portrayed with diagrams using standard symbols, showing interconnections among their components. We ve seen wires, capacitors, and resistors so far EMF, or electromotive force, is a device that creates a potential difference between its sides. For example, a battery or power supply It supplies electrical energy It has a + side and a side Current flows from + to on an EMF or battery (Remember that electrons flow the opposite way) Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 16

17 Ground and Grounding One of the electrical symbols above was for ground All wires connected to ground have an electric potential of zero Current flows from positive potential to ground Current flows from ground to negative potential > 0 I This is the electrical equivalent of us setting electric potential to zero at infinity (or very far away) Ground wants to make stuff electrically neutral Ground can be a source or sink of an effectively infinite amount of electrical charges or current Think of it as a vast conductor with many charges Perhaps as vast as the earth Hmm, maybe that s why it s called ground» ya think? ( = 0) I < 0 I wonder how small this font gets Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 17

18 Back to Resistors Just like capacitors, we ll have to deal with resistors in series and parallel Our important principles still hold true, but now for resistors! Elements that are in parallel have the same voltage They share the same conductors on both sides But they can (and often do) have different current I 1 I = I 1 + I 2 Elements that are in series have the same current Or, for capacitors, the same charge But they can (and often do) have different voltages I I I = Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 18

19 Connecting Resistors in Series Here the resistors have the same current I but different voltages 1 and 2 Same current I in both resistors 1 = IR 1 = IR 1 2 R 1 R 2 2 = IR 2 = IR = IR +1+IR 2 R = R 1 + R 2 Equivalent resistance R = IR Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 19

20 Connecting Resistors in Parallel Here the resistors have the same potential difference but different currents I I = I 1 + I 2 I 1 = R 1 = IR I 1 I 2 R 1 R 2 I 2 = R 2 I I = I 1 + I 2 R = R 1 + R 2 1 R = 1 R R 2 Equivalent resistance R I = R Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 20

21 Analyzing Circuits with Series and Parallel Components Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 21

22 Multiloop Circuits Some circuits aren t amenable to series-parallel analysis. Then it s necessary to use Kirchhoff s loop and node laws: The loop law states that the sum of voltage drops around any circuit loop is zero. The loop law expresses conservation of energy. The node law states that the sum of currents at any circuit node is zero. The node law expresses conservation of charge. Node and loop equations for this circuit: I + I + I = 0 (node A) I I = 0 (loop 1) I I = 0 (loop 2) 2 3 Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 22

23 Electrical Measurements: oltage A voltmeter measures the potential difference between its two terminals. Connect a voltmeter in parallel with the component whose voltage you re measuring. An ideal voltmeter has infinite resistance so it doesn t affect the circuit being measured. A real voltmeter should have a resistance much greater than resistances in the circuit being measured. Correct (a) and incorrect (b) ways to measure the voltage across R 2 Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 23

24 Electrical Measurements: Current An ammeter measures the current flowing through itself. Connect an ammeter in series with the component whose current you re measuring. An ideal ammeter has zero resistance so it doesn t affect the circuit being measured. A real ammeter should have a resistance much less than resistances in the circuit being measured. Correct (a) and incorrect (b) ways to measure the current in the series circuit Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 24

25 Capacitors in Circuits Capacitors introduce time-dependent behavior to circuits. The voltage across a capacitor is proportional to the charge on the capacitor. The charge can t change instantaneously, because that would require an infinite current to move a finite amount of charge onto the capacitor in zero time. Therefore, the voltage across a capacitor cannot change instantaneously. Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 25

26 The RC Circuit The capacitor voltage C is initially zero. Therefore, current flows through the resistor, putting charge on the capacitor. As the capacitor charges, C increases and the voltage across the resistor decreases. Therefore, the current decreases. Eventually a steady state is reached, with zero current and capacitor voltage equal to the battery emf. Prof. Satogata / Spring 2014 ODU University Physics 227N/232N 26

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