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 Δ x is – Where n is the number of charge carriers per unit volume and q is the charge carried by each.

7. 27.1

8. If the carriers move with a speed of v d, (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/m 2

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/ σ A 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 ρ is the resistivity at temperature T (in o C), ρ o is the resistivity at temperature T o, 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, T c. The material often acts like a normal conductor above T c, but falls of to zero, below T c.

26. 27.5

27. There are basically two recognized types of superconductors – Metals very low T c. – Ceramics much higher T c.

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 = Q Δ V, 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 ( Δ V = 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