Chapter 20 Capacitors Resistors and Batteries Real Batteries
Chapter 20 Capacitors, Resistors and Batteries
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:
Real Batteries: Internal Resistance ideal battery Model of a real battery Round trip (energy conservation): Situation 1: disconnect R (R= ) R I=0 V = emf Situation 2: R is in place Situation 3: short battery (R=0) I = emf /rint V = 0
Real Batteries: Internal Resistance ideal battery R rint 0. 25 1. 5 V R 100 1 0 Ideal 0. 015 A 0. 15 A 1. 5 A infinite Real 0. 01496 A 0. 146 A 1. 2 A 6 A VR=RI 1. 496 V 1. 46 V 1. 2 V 0 V
Ammeters, Voltmeters and Ohmmeters Ammeter: measures current I Voltmeter: measures voltage difference V Ohmmeter: measures resistance R
Using an Ammeter 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. 0. 150 Conventional current must flow into the ‘+’ terminal and emerge from the ‘-’ terminal to result in positive reading.
Exercise: Connecting Ammeter Is it correct connection? A) Yes B) No
Voltmeters measure potential difference VAB – add a series resistor to ammeter Measure I and convert to VAB=IR Connecting Voltmeter: Higher potential must be connected to the ‘+’ socket and lower one to the ‘-’ socket to result in positive reading.
Voltmeter: Internal Resistance VAB in absence of a voltmeter R 1 emf B rint R 2 VAB in presence of a voltmeter A A Internal resistance of a voltmeter must be very large
Demonstration
Clicker What is the potential difference across the clams when I take bulb out of circuit? A) 1. 7 V B) 3. 4 V C) 5. 1 V D) 6. 8 V E) 12 V
Quantitative Analysis of an RC Circuit Initial situation: Q=0 Q and I are changing in time
RC Circuit: Current in an RC circuit What is I 0 ? Current in an RC circuit
RC Circuit: Charge and Voltage What about charge Q on capacitor? Current in an RC circuit Check: t=0, Q=0, t--> inf, Q=C*emf
RC Circuit: Summary Current in an RC circuit Charge in an RC circuit Voltage in an RC circuit
The RC Time Constant 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. A rough measurement of how long it takes to reach final equilibrium
What is the value of RC? About 9 seconds
Exercise: A Complicated Resistive Circuit Find currents through resistors I 2 loop 1: Loop 2 loop 2: I 1 I 3 Loop 1 Loop 3 I 4 Loop 4 loop 3: I 5 nodes: Five independent equations and five unknowns
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