Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 25 Current, Resistance, and Electromotive Force

Copyright © 2012 Pearson Education Inc. Goals for Chapter 25 To understand current and how charges move in a conductor To understand resistivity and conductivity To calculate the resistance of a conductor To learn how an emf causes current in a circuit To calculate energy and power in circuits

Copyright © 2012 Pearson Education Inc. Current Current is any motion of charge from one region to another. Current I = dQ/dt [Amps] E field in conductor causes charges to flow.

Copyright © 2012 Pearson Education Inc. Direction of current flow A current can be produced by positive or negative charge flow. Conventional current is treated as a flow of positive charges. The moving charges in metals are electrons (see figure below).

Copyright © 2012 Pearson Education Inc. Current, drift velocity, and current density Suppose: –n charged particles/volume –move w/ drift velocity v d –In time element dt –Cross-sectional area A dQ = q (nAv d dt) I = dQ/dt = nqAv d (scalar) Define current density J –J = I/A = nqv d (vector)

Copyright © 2012 Pearson Education Inc. Current, drift velocity, and current density Example: –18 gauge wire (diameter = 1.02 mm); –current 1.67 A – 200 Watt lamp –Electron density = 8.5 x /m 3. What is J and v d ?

Copyright © 2012 Pearson Education Inc. Resistivity Resistivity of material = ratio of E field in material to current density it causes:  = E/J. Large  implies a large E field is needed to generate small current!

Copyright © 2012 Pearson Education Inc. Resistivity Conductivity is the reciprocal of the resistivity. High conductivity means a large current results from a small applied E field.

Copyright © 2012 Pearson Education Inc. Resistivity and temperature Resistivity depends on temperature. ~ Linear R(T) = R 0 [1+  (T-T 0 )] Table 25.2 shows some temperature coefficients of resistivity.

Copyright © 2012 Pearson Education Inc. Resistance Resistance of a conductor is R =  L/A [Ohms] Potential decreases across a conductor is V = IR Going from higher V to lower; in direction of current V = IR (Ohm’s Law)

Copyright © 2012 Pearson Education Inc. Resistors are color-coded for easy identification This resistor has a resistance of 5.7 kΩ with a tolerance of ±10%.

Copyright © 2012 Pearson Education Inc. Ohmic and nonohmic resistors Only the resistor in Figure 25.10(a) below obeys Ohm’s law.

Copyright © 2012 Pearson Education Inc. Electromotive force and circuits An electromotive force (emf) makes current flow. In spite of the name, an emf is not a force. For simple complete circuits, EMF “pushes” current around from start to finish. “EMF” is a voltage difference! Ideal source – EMF is constant V ab = E

Copyright © 2012 Pearson Education Inc. Electromotive force and circuits Source of emf in an open circuit (left) Source of EMG in complete circuit (right).

Copyright © 2012 Pearson Education Inc. Internal resistance Real sources of emf actually contain some internal resistance r. The terminal voltage of an emf source is V ab =  – Ir. Terminal voltage of 12-V battery is less than 12 V when actually connected to the light bulb.

Copyright © 2012 Pearson Education Inc. Symbols for circuit diagrams Table 25.4 shows the usual symbols used in circuit diagrams.

Copyright © 2012 Pearson Education Inc. Example 25.4 EMF = 12 V; internal r = 2 Ohms. What do ideal Voltmeter and Ammeter read?

Copyright © 2012 Pearson Education Inc. Source in a complete circuit Now add a 4-Ohm resistor to the same source….

Copyright © 2012 Pearson Education Inc. Source in a complete circuit Now add a 4-Ohm resistor to the same source…. Ideal I = 12V/6  = 2 A V = IR = 2A x 4  = 8V V = 12V – 2A x 2  = 8V

Copyright © 2012 Pearson Education Inc. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits?

Copyright © 2012 Pearson Education Inc. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Ammeters measure flow of current PAST a point. Ideally, they should NOT influence the current Ideally, R (ammeter) = 0! Put them IN SERIES with circuit “legs”

Copyright © 2012 Pearson Education Inc. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Voltmeters measure pressure difference across (or between) points in the circuit. Ideally, they should NOT influence the current Ideally, R (voltmeter) =  ! Put them in parallel!

Copyright © 2012 Pearson Education Inc. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits?

Copyright © 2012 Pearson Education Inc. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Voltmeter in Series! R(voltmeter) =  No current will flow!

Copyright © 2012 Pearson Education Inc. A source with a short circuit Without a resistor, what happens?

Copyright © 2012 Pearson Education Inc. Potential changes around a circuit “Loop Rule”: –NET change in potential = zero for round trip in a circuit EMF for loop equals sum of voltage “drops” across resistors or other elements.

Copyright © 2012 Pearson Education Inc. Energy and power in electric circuits Rate energy is delivered to (or extracted from) a circuit element is P = V ab I. [POWER] = [WATTS] Power delivered to pure resistor: P = I 2 R = V ab 2 /R.

Copyright © 2012 Pearson Education Inc. Energy and power in electric circuits Rate energy is delivered to (or extracted from) a circuit element is P = V ab I. [POWER] = [WATTS] Power delivered to pure resistor: P = I 2 R = V ab 2 /R.

Copyright © 2012 Pearson Education Inc. Power input and output What are rates of energy conversion and power dissipation in circuit?

Copyright © 2012 Pearson Education Inc. Power input and output What are rates of energy conversion and power dissipation in circuit? –Battery provides E I = 12 V x 2A = 24 Watts –Energy dissipation in battery = I 2 r = 8 Watts –Energy dissipation in 4  resistor = 16 Watts

Copyright © 2012 Pearson Education Inc. Power in a short circuit Now power = 12 V x 6A = 72 W = I 2 R (internal)

Copyright © 2012 Pearson Education Inc. Theory of metallic conduction Random motion of electrons in a conductor.

Copyright © 2012 Pearson Education Inc. PGE Rates & Meanings…. PGE rates (10/3/12): Small Businesses –$0.151/KWh (peak) –$0.136/KWh (off peak) Home rates –$0.13/KWh (baseline to 351 kWh, winter) –$.034/KWh (max) What’s a KWh??

Copyright © 2012 Pearson Education Inc. PGE Rates & Meanings…. What’s a KWh?? Kilowatt = 1000 Watts = 1000 Joules/Second Kilowatt-hour = 1000 Watts x 3600 seconds = 3.6 x 10 6 Joules = 3.6 MegaJoules = 3.6 MJ How much energy do I use? 100W light bulb 5 hours at night to study physics? 0.1 KW x 5 hours = 0.5 $.13/KWh Only 6.5 CENTS!!! (See!! Study physics!)

Copyright © 2012 Pearson Education Inc. PGE Rates & Meanings…. What’s a KWh?? Kilowatt = 1000 Watts = 1000 Joules/Second Kilowatt-hour = 1000 Watts x 3600 seconds = 3.6 x 10 6 Joules = 3.6 MegaJoules = 3.6 MJ How much energy do I use? 100W light bulb 5 hours at night to study physics? 0.1 KW x 5 hours = 0.5 $.13/KWh Only 6.5 CENTS!!! (See!! Study physics!)

Copyright © 2012 Pearson Education Inc. What do we use on average in the US? ~ 960 KWh/residence/month 2 (electricity) ~ 12,000 KWh/year ~ 80K – 90K KWh ( MWh) of energy from all sources per person per year 1 Sources: 1 US Department of Energy [Internet]. How much electricity does an American home use? 2012 Oct Wikipedia contributors. Energy in the United States [Internet]. Wikipedia, The Free Encyclopedia; 2012 Oct 12:48 UTC [cited 2012 Oct 3]. Available from: 2