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Capacitors, Multimeters, Circuit Analysis

Capacitors, Multimeters, Circuit Analysis. Capacitor: Charging and Discharging. Charging. Discharging. Capacitor: Construction and Symbols. The capacitor in your set is similar to a large two-disk capacitor. D. s. There is no connecting path through a capacitor.

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Capacitors, Multimeters, Circuit Analysis

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  1. Capacitors, Multimeters, Circuit Analysis

  2. Capacitor: Charging and Discharging Charging Discharging

  3. Capacitor: Construction and Symbols The capacitor in your set is similar to a large two-disk capacitor D s There is no connecting path through a capacitor

  4. How is Discharging Possible? Positive and negative charges are attracted to each other: how can they leave the plates? Fringe field is not zero! Electrons in the wire near the negative plate feel a force that moves them away from the negative plate. Electrons near the positive plate are attracted towards it.

  5. Capacitor: Charging Why does current ultimately stop flowing in the circuit? Ultimately, the fringe field of the capacitor and the field due to charges on the wire are such that E=0 inside the wire. At this point, i=0.

  6. The Effect of Different Light Bulbs Thin filament Thick filament Which light bulb will glow longer? Why? • Round is brighter  capacitor gets charged more? 2) Long bulb glows longer  capacitor gets charged more?

  7. An Isolated Light Bulb Will it glow at all? How do electrons flow through the bulb? Why do we show charges near bulb as - on the left and + on the right?

  8. Capacitance -Q +Q E s Electric field in a capacitor: In general: Definition of capacitance: Capacitance of a parallel-plate capacitor: Capacitance

  9. Capacitance Units: C/V, Farads (F) Michael Faraday (1791 - 1867)

  10. Exercise The capacitor in your set is equivalent to a large two-disk capacitor D s=1 mm How large would it be? D ~ 10 km (6 miles)

  11. Exercise A capacitor is formed by two rectangular plates 50 cm by 30 cm, and the gap between the plates is 0.25 mm. What is its capacitance?

  12. A Capacitor With an Insulator Between the Plates D s No insulator: With insulator:

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

  14. Using an Ammeter 0.150 Connecting ammeter: Conventional current must flow into the ‘+’ terminal and emerge from the ‘-’ terminal to result in positive reading.

  15. Ammeter Design Simple ammeter using your lab kit: Simple commercial ammeter Digital ammeters: uses semiconductor elements. ADC – analog-to-digital converter (Combination of comparator and DAC)

  16. Voltmeter 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.

  17. Ohmmeter A R Ohmmeter How would you measure R? Ammeter with a small voltage source

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

  19. RC Circuit: Current Current in an RC circuit Current in an RC circuit What is I0 ?

  20. RC Circuit: Charge and Voltage Current in an RC circuit What about charge Q?

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

  22. 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

  23. What is the value of RC? About 9 seconds

  24. Question

  25. A B D C

  26. Exercise Current in an RC circuit What is the final charge on a 1 F capacitor connected to a 1.5V battery through resistor 100 ? Can you apply the RC equations to the circuit below? No! Resistance depends on current.

  27. Exercise: A Complicated Resistive Circuit I2 I1 I3 Loop 1 Loop 2 Loop 3 I4 I5 Loop 4 Find currents through resistors loop 1: loop 2: loop 3: nodes: Five independent equations and five unknowns

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