Chapter 20 Capacitors Resistors and Batteries Capacitance of

Chapter 20 Capacitors, Resistors and Batteries

Capacitance of parallel plate capacitor: A=area, s-separation between plates Select a correct formula: 1. C = A* 0/s 2. C = A/ 0 s 3. C = 0/(A*s) 4. C = s/ 0 A

Macroscopic Analysis of Circuits Microscopic treatment: insight into the fundamental physical mechanism of circuit behavior. Not easy to measure directly E, u, Q, v. It is easier to measure conventional current, potential difference macroscopic parameters Need a link between microscopic and macroscopic quantities.

Resistance Many elements in a circuit act as resistors: prevent current from rising above a certain value. Goal: find a simple parameter which can predict V and I in such elements. Need to combine the properties of material and geometry.

Conductivity Combining the properties of a material Geometry Conventional current: Different properties of the material Group the material properties together: Current density: Conductivity

Exercise In copper at room temperature, the mobility of electrons is about 4. 5. 10 -3 (m/s)/(V/m) and the density of electrons is n=8. 1028 m-3. What is ? What is the strength of E required to drive a current of 0. 3 A through a copper wire which has a cross-section of 1 mm 2 ?

Exercise The conductivity of tungsten at RT is =1. 8. 107 (A/m 2)/(V/m) and it decreases 18 times at a temperature of a glowing filament (3000 K). The tungsten filament has a radius of 0. 015 mm. What is E required to drive 0. 3 A through it?

Conductivity with two kinds of charge carriers

Resistance Conventional current: Widely known as Ohm’s law Resistance of a long wire: George Ohm (1789 -1854) Units: Ohm, Resistance combines conductivity and geometry!

Microscopic and Macroscopic View Microscopic Macroscopic Can we write V=IR ? Current flows in response to a V

Exercise: Carbon Resistor A = 0. 002 mm 2 L=5 mm Conductivity of Carbon: = 3. 104 (A/m 2)/(V/m) What is its resistance R? (V/A) What would be the current through this resistor if connected to a 1. 5 V battery?

Constant and Varying Conductivity Mobility of electrons: depends on temperature Conductivity and resistance depend on temperature. Conductivity may also depend on the magnitude of current.

Ohmic Resistors Ohmic resistor: resistor made of ohmic material Ohmic materials: materials in which conductivity is independent of the amount of current flowing through not a function of current Examples of ohmic materials: metal, carbon (at constant T!)

Is a Light Bulb an Ohmic Resistor? Tungsten: mobility at room temperature is larger than at ‘glowing’ temperature (~3000 K) V-A dependence: 3 V 100 m. A 1. 5 V 80 m. A 0. 05 V 6 m. A R 30 19 8 I V

Semiconductors Metals, mobile electrons: slightest V produces current. If electrons were bound – we would need to apply some field to free some of them in order for current to flow. Metals do not behave like this! Semiconductors: n depends exponentially on E Conductivity rises (resistance drops) with rising temperature

Nonohmic Circuit Elements Semiconductors | V|=Q/C, function of time Capacitors Batteries: double current, but | V| emf, hardly changes has limited validity! Ohmic when R is indeppendent of I! Conventional symbols:

Series Resistance Vbatt + V 1 + V 2 + V 3 = 0 emf - R 1 I - R 2 I - R 3 I = 0 emf = R 1 I + R 2 I + R 3 I emf = (R 1 + R 2 + R 3) I emf = Requivalent I , where Requivalent = R 1 + R 2 + R 3 For resistors made of the same material and with the same A it follows straight from the definition of resistance:

Parallel Resistance I = I 1 + I 2 + I 3 For resistors made of the same material and with the same A it follows straight from the definition of resistance:

Question I 1 I 2 Identical bulbs are connected to identical set of batteries. They produce light. Compare I 1 and I 2 : A. I 1 = I 2 B. I 1 slightly less than I 2 C. I 1 = 2*I 2 D. I 1 slightly less than 2*I 2

Real Batteries: Internal Resistance Drift speed of ions in chemical battery: In usual circuit elements: rint - internal resistance In a battery: emf , assuming uniform field: