Chapter 20 A Microscopic View of Electric Circuits

Announcements: March 31th last day for EXAM 1 free response re-take. Second midterm April 3 rd, Thursday, 8-9:30 pm, room 203 No lecture on April 9 th

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

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!) Ohmic Resistors

Tungsten: mobility at room temperature is larger than at ‘glowing’ temperature (~3000 K) V-A dependence: 3 V100 mA 1.5 V 80 mA 0.05 V 6 mA R 30  19  8  VV I Is a Light Bulb an Ohmic Resistor?

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 depends exponentially on E Conductivity of semiconductor rises (resistance drops) with rising temperature Semiconductors

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

 V batt +  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 = R equivalent I, where R equivalent = 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: Series 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: Parallel Resistance

Question 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 I1I1 I2I2

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

Model of a real battery ideal battery R Round trip (energy conservation): Real Batteries: Internal Resistance Situation 1: disconnect R (R=  ) I = 0  V = emf Situation 2: R is in place Situation 3: short battery (R=0)I = emf /r int  V = 0

ideal battery R r int  0.25  R 100  10  1  0  Ideal A 0.15 A 1.5 A infinite 1.5 V Real A A 1.2 A 6 A  V R =RI V 1.46 V 1.2 V 0 V Real Batteries: Internal Resistance

What is the maximum current? For one: Two batteries: Two batteries in series: short-circuit current is the same as for one (internal resistance is twice higher) Two Batteries in Series

What is the maximum current? I 3 = I 1 + I 2 I1I1 I2I2 For one: Two batteries: Two batteries in parallel: short-circuit current is twice of one (or internal resistance is twice smaller than that of one) Two Batteries in Parallel

Ammeter: measures current I Voltmeter: measures voltage difference  V Ohmmeter: measures resistance R Ammeters, Voltmeters and Ohmmeters

0.150 Connecting ammeter: An ammeter must be inserted into the circuit in series with the circuit element whose current you want to measure. An ammeter must have a very small resistance, so as not to alter significantly the circuit in which it has been inserted. Conventional current must flow into the ‘+’ terminal and emerge from the ‘-’ terminal to result in positive reading. Using an Ammeter

Is it correct connection? A)Yes B)No Exercise: Connecting Ammeter

 V AB – add a series resistor to ammeter Measure I and convert to  V AB =IR Connecting Voltmeter: Higher potential must be connected to the ‘+’ socket and lower one to the ‘-’ socket to result in positive reading. Voltmeter Voltmeters measure potential difference

R1R1 R2R2 emf A B  V AB in absence of a voltmeter A r int  V AB in presence of a voltmeter Internal resistance of a voltmeter must be very large Voltmeter: Internal Resistance

Initial situation: Q=0 Q and I are changing in time Quantitative Analysis of an RC Circuit

Current in an RC circuit What is I 0 ? Current in an RC circuit RC Circuit: Current

Current in an RC circuit What about charge Q on capacitor? Current in an RC circuit RC Circuit: Charge and Voltage Check: t=0, Q=0, t--> inf, Q=C*emf

Current in an RC circuit Charge in an RC circuit Voltage in an RC circuit RC Circuit: Summary

Current in an RC circuit When time t = RC, the current I drops by a factor of e. RC is the ‘time constant’ of an RC circuit. The RC Time Constant A rough measurement of how long it takes to reach final equilibrium

What is the value of RC? About 9 seconds

Find currents through resistors Loop 1Loop 2Loop 3 Loop 4 I1I1 I2I2 I3I3 I5I5 I4I4 loop 1: loop 2: loop 3: nodes: Five independent equations and five unknowns Exercise: A Complicated Resistive Circuit