Current�and�Resistance

1. Current�and�Resistance Electric Current Resistance and Ohm’s Law A Model for Electrical Conduction Resistance and Temperature Superconductor Electrical Energy and Power

2. Electric Current • Suppose  that  the  charges are moving perpendicular  to a  surface of area A • The current  is  the  rate at which charge flows  through  this  surface • The average current • The Instantaneous current is • The SI unit of current is the ampere (A):

3. Electric Current (2) • It is conventional to assign to the current the  same direction as the flow of positive charge • In electrical conductors, the direction ofthe current is opposite the direction of flow of electrons • Itis common to refer to a moving charge(positive or negative) as a mobile charge carrier

4. Microscopic Model of Current • We can relate current to the motion of the charge carriers by describing a microscopic model of  conduction  in  a metal • The  volume  of  a  section  of  the  conductor  of length is • If n represents thenumber of mobile charge carriers per unit volume, the number of  carriers  in  the gray section is • If the charge of each carrier is q, total charge in the section is

5. Microscopic Model of Current (2) • If the carrier moves with the speed , the distance during is , thus • The average current  in theconductoris • The speed of the charge carriers vdis an average speed called the drift speed

6. RESISTANCE AND OHM’S LAW • We know that average current is • The current density J • In some materials, the current density is proportional to the electric field: • The constant is called conductivity. It is well-known as ohm’s law • Materials that obey Ohm’s law is said to be ohmic

7. RESISTANCE AND OHM’S LAW (2) • The potential difference between a and b is • We can rewrite the current density as • Because then the potential difference • The quantity  is called the resistance R of the conductor • The unit of R is ohm (volt/ampere)

8. RESISTANCE AND OHM’S LAW (3) • The inverse of conductivity is resistivity

9. Various Resistance

10. A MODEL FOR ELECTRICAL CONDUCTION • This models describes the connection between resistivity and electron movement in conductor. • In absence of E, the electron moves randomly. The net movement is zero. Thus the drift velocity is zero (Fig. a) • An E modifies the random motion and causes  the  electrons  to  drift  in  a  direction  opposite  that  of E • The slight curvature in the paths shown in Fig.bresults from the acceleration of the electrons between collisions • Theacceleration of the electron is • The electron will gain velocity

11. A MODEL FOR ELECTRICAL CONDUCTION (2) • Suppose that vi=0 and is the average value of successive collision, then the drift velocity • The magnitude of the current density is • Comparing with ohm’s law

12. RESISTANCE AND TEMPERATURE • The  resistivity of  a metal  varies  approximately linearly with temperature according to the expression • The variation of resistanceas • T0 is normally 20o C

13. SUPERCONDUCTORS

14. ELECTRICAL ENERGY AND POWER • When net positive charge moves from a to b, it gains electric potential energy . The chemical potential energy in battery decreases. • As the charge travels from c to d, it losses the electric potential energy due to the collision with resistor’s atom. • The rates is • The energy lost in resistor is equal energy transferred by battery

15. ELECTRICAL ENERGY AND POWER • The resistor’s voltage is , thus other formulas for energy in capacitor • A battery is an emf source

16. Resistor in Serial • Resistors connected in serial have the same flowing current I = I1 = I2 = I3 V = V1+ V2 + V3 I Rt= I1R1 + I2R2 + I3R3 V Rt= R1 + R2 + R3

17. Resistor in Parallel • Resistors in parallel have the same voltage’s magnitude • V = V1 = V2 = V3 • It = I1 + I2 + I3 • V/Rt = V/R1 + V/R2 + V/R3 • 1/Rt = 1/R1 + 1/R2 + 1/R3 V