Chapter 27

1. Chapter 27 Current and Resistance

2. Intro • Up until now, our study of electricity has been focused Electrostatics (charges at equilibrium conditions). • We will now look at non-equilibrium conditions, and we will define electric current as the rate of flow of charge. • We will look at current at the microscopic levels and investigate factors oppose current as well.

3. 27.1 Electric Current • Current- any net flow of charge through some region. • A similar analogy would be water current, or the volume of water flowing past a given point per unit time (shower heads, rivers etc.) • The rate of charge passing perpendicularly through a given area.

4. 27.1 • The average current • The instantaneous current • The SI unit of current is the Ampere (A)

5. 27.1 • Current Direction- • Traditional- in the direction the flow of positive charge carriers. • Conducting Circuits- Electrons are the flowing charge, current is in the opposite direction of the flow of negative charge carriers (electrons). • Particle Accelerator- with the beam of positive charges • Gases and Electrolytes- the result of both positive and negative flowing charge carriers.

6. 27.1 • At the microscopic level we can relate the current, to the motion of the charge carriers. • The charge that passes through a given region of area A and length Δx is • Where n is the number of charge carriers per unit volume and q is the charge carried by each.

7. 27.1

8. 27.1 • If the carriers move with a speed of vd, (drift velocity) such that and • So the passing charge is also given as

9. 27.1 • If we divide both sides by time we get another expression for average current

10. 27.1 • Drift Velocity- • Charge carrier: electron • The net velocity will be in the opposite direction of the E-field created by the battery

11. 27.1 • We can think of the collisions as a sort of internal friction, opposing the motion of the electrons. • The energy transferred via collision increases the Avg Kinetic Energy, and therefore temperature. • Quick Quiz p 834 • Example 27.1

12. 27.2 Resistance • E-Field in a conductor = 0 when at equilibrium ≠ 0 under a potential difference • Consider a conductor of cross-sectional area A, carrying a current I. • We can define a new term called current density • Units A/m2

13. 27.2 • Because this current density arises from a potential difference across, and therefore an E-field within the conductor we often see • Many conductors exhibit a Current density directly proportional to the E-field. • The constant of proportionality σ, is called the “conductivity”

14. 27.2 • This relationship is known as Ohm’s Law. • Not all materials follow Ohm’s Law • Ohmic- most conductors/metals • Nonohmic- material/device does not have a linear relationship between E and J.

15. 27.2 • From this expression we can create the more practical version of Ohm’s Law • Consider a conductor of length l

16. 27.2 • So the voltage equals • The term l/σA will be defined as the resistance R, measured in ohms (1 Ω = 1 Volt/Amp)

17. 27.2 • We will define the inverse of the conductivity (σ) as the resistivity (ρ) and is unique for each ohmic material. • The resistance for a given ohmic conductor can be calculated

18. 27.2 • Resistors are very common circuit elements used to control current levels. • Color Code

19. 27.2 • Quick Quizzes, p. 838-839 • Examples 27.2-27.4

20. 27.4 Resistance and Temperature • Over a limited temperature range, resistivity, and therefore resistance vary linearly with temperature. • Where ρis the resistivity at temperature T (in oC), ρo is the resistivity at temperature To, and α is the temperature coefficient of resistivity. • See table 27.1 pg 837

21. 27.4 • Since Resistance is proportional to resistivity we can also use

22. 27.4 • For most conducting metals the resistivity varies linearly over a wide range of temperatures. • There is a nonlinear region as T approaches absolute zero where the resitivity will reach a finite value.

23. 27.4 • There are a few materials who have negative temperature coefficients • Semiconductors will decrease in resistivity with increasing temps. • The charge carrier density increases with temp.

24. 27.4 • Quick Quiz p 843 • Example 27.6

25. 27.5 Superconductors • Superconductors- a class of metals and compounds whose resistance drops to zero below a certain temperature, Tc. • The material often acts like a normal conductor above Tc, but falls of to zero, below Tc.

26. 27.5

27. 27.5 • There are basically two recognized types of superconductors • Metals very low Tc. • Ceramics much higher Tc.

28. 27.5 • Electric Current is known to continue in a superconducting loop for YEARS after the applied potential difference is removed, with no sign of decay. • Applications: Superconducting Magnets (used in MRI)

29. 27.6 Electrical Power • When a battery is used to establish a current through a circuit, there is a constant transformation of energy. • Chemical  Kinetic  Internal (inc. temp) • In a typical circuit, energy is transferred from a source (battery) and a device or load (resistor, light bulb, etc.)

30. 27.6 • Follow a quanity of charge Q through the circuit below. • As the charge moves from a to b, the electric potential energy increase by U = QΔV, while the chemical potential energy decrease by the same amount.

31. 27.6 • As the charge moves through the resistor, the system loses this potential energy due to the collisions occuring within the resistor. (Internal/Temp) • We neglect the resistance in the wires and assume that any energy lost between bc and da is zero.

32. 27.6 • This energy is then lost to the surroundings. • The rate at which the system energy is delivered is given by • Power the rate at which the battery delivers energy to the resistor.

33. 27.6 • Applying the practical version of Ohm’s Law (ΔV = IR) we can also describe the rate at which energy is dissipated by the resistor. • When I is in Amps, V is in Volts, and R is in Ohms, power will be measured in Watts.

34. 27.6 • Quick Quizzes p. 847 • Examples 27.7-27.9