Current. Lecture 10. Chapter Physics II. Course website:

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1 Lecture 10 Chapter 30 Physics II Current Course website: Lecture Capture:

2 A Model of Conduction Up to this point we were talking about electrostatic equilibrium when a conductor was at the same potential and there was no current. In this case, an electron bounces back and forth between collisions, but its average velocity is zero. Now if we add a battery, a potential difference will be imposed and the electrons will start travelling creating a current

3 Current (definition) If Q is the total amount of charge that has moved past a point in a wire, we define the current I in the wire to be the rate of charge flow: current is the rate at which charge flows dq The SI unit for current is the coulomb per second, which is called the ampere. 1 ampere = 1 A = 1 C/s.

4 Direction of current (convention) By convention, current is defined as flowing of motion positive particles from + to -. Electrons actually flow in the opposite direction. Current (by convention motion of positive particles) Current Current flows from a positive terminal of a battery to a negative one.

5 Every minute, 120 C of charge flow through this cross section of the wire. The wire s current is ConcepTest 1 Current A) 240 A B) 120 A C) 60 A D) 2 A E) Some other value.

6 The Current Density in a Wire A The current density J in a wire is the current per square meter of cross section: The current density has units of A/m 2.

7 Conservation of Current For a junction, the law of conservation of current requires that I out1 I in1 I in I out2 I in =I out1 +I out2 I in1 +I in2 =I out I in2 I out This basic conservation statement is called Kirchhoff s junction law.

8 ConcepTest 2 The current in the fourth wire is Conservation of Current A) 16 A to the right B) 4 A to the left C) 2 A to the right D) 2 A to the left E) Not enough information to tell For a junction, the law of conservation of current requires that Assume I x is out (to the right) 2 A+5 A=9 A+I x I x = -2 A So, the assumption that I x is to the right was wrong. It is to the left. I x

9 Resistance Ohm s Law

10 Ohm s Law Consider a piece of wire. For a current to exist, there must be a potential difference between its ends (just as a difference in height between source and outlet is necessary for a river current to exist) If we keep changing V and measure I and plot it, we will get a straight line. So V ~ I The coefficient of proportionality is called the electrical resistance, R V The SI unit of resistance is the ohm. 1 ohm 1 1 V/A Ohm s Law is not a fundamental law but is an experimental relationship that metals obey. V

11 ConcepTest 3 Resistor A) A>B Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? B) B>A C) A=B Current flows from a positive terminal of a battery to a negative one. Current (b) Is the current greater at point A or at point B? A) A>B B) B>A C) A=B

12 ConcepTest 4 Both segments of the wire are made of the same metal. Current I 1 flows into segment 1 from the left. How does current I 1 in segment 1 compare to current I 2 in segment 2? Resistor A) I 1 > I 2 B) I 1 = I 2 C) I 1 < I 2 D) There s not enough information to compare them How about current density J? J 1 J 2. Since A 1 A 2 then

13 Ohm s Law Let s look deeper in Resistance

14 Resistivity Consider a cylindrical piece of wire/resistor: A L ρ called the resistivity and depends on the material used We define the resistance R of a long, thin conductor of length L and cross-sectional area A to be: Units The reciprocal of the resistivity is called the conductivity

15 Resistance vs- Resistivity Resistivity (ρ) describes only the material (Au, Co, ). Resistance (R) characterizes a specific piece of the conductor with a specific geometry

16 Problem 14

17 Example

18 Example (cont.)

19 ConcepTest 5 Two wires, A and B, are made of the same metal and have equal length, but the resistance of wire A is four times the resistance of wire B. How do their areas compare? Wires I A. = B. = 2 C. D. 4 = E. 2 = (area) (area) L The resistance of wire A is greater because its area is less than wire B. ratio

20 What you should read Chapter 30 (Knight) Sections

21 Thank you See you on Friday