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Chapter 28

Chapter 28. Direct Current Circuits. Introduction. In this chapter we will look at simple circuits powered by devices that create a constant potential difference across their terminals. Most of our circuits will exist in a “Steady State” meaning a constant current in the same direction.

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Chapter 28

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  1. Chapter 28 Direct Current Circuits

  2. Introduction • In this chapter we will look at simple circuits powered by devices that create a constant potential difference across their terminals. • Most of our circuits will exist in a “Steady State” meaning a constant current in the same direction. • These are known as “Direct Current” or DC circuits.

  3. 28.1 Electromotive Force • Batteries are often referred to as a source of emf or electromotive force. • The emf, ε, of a battery is the maximum possible voltage that the battery can provide across its terminals. • Its not really a force • Think of it as a charge pump.

  4. 28.1 • When connected in a circuit, the terminal voltage of a real battery is typically less than its emf. • This is due to the internal resistance (r) found in a real battery. • Ideal Batteries have zero internal resistance.

  5. 28.1 • Look at a simple circuit, battery and resistor.

  6. 28.1 • The current created will equal the terminal voltage divided by the load resistance (R) from Ohm’s Law. • To find the emf of the battery we need to realize that some of the potential is dropped by the internal resistance and the rest is dropped by the load resistance.

  7. 28.1

  8. 28.1 • The emf is given as • The current in the circuit is therefore • And the total power output of the battery is

  9. 28.1 • Quick Quiz p 860 • Examples 28.1 and 28.2

  10. 28.2 Resistors in Series and Parallel • For a series combination of two resistors • The current through each resistor is the same (All charges must pass through both resistors)

  11. 28.2 • The potential difference across both resistors is given as • So the equivalent resistance for series combinations is given as

  12. 28.2 • Quick Quizzes p. 863

  13. 28.2 • For a parallel combination of two resistors • The current can split at a junction. • The Sum of currents leaving the junction, will equal the total entering.

  14. 28.2 • Since both resistors are connected directly across the terminals of the battery, the potential difference across each resistor is the same.

  15. 28.2 • To find the equivalent resistance…

  16. 28.2 • To Recap Series Combinations: • To Recap Parallel Combinations

  17. 28.2 • Quick Quizzes p. 865 • Examples 28.3-28.7

  18. 28.3 Kirchoff’s Rules • Simple Circuits can be analyzed using • Ohm’s Law • Series/Parallel Rules • If the circuit cannot be reduced to a single loop, we will use Kirchoff’s Rules to analyze. • Junction Rule • Loop Rule

  19. 28.3 • Junction Rule- The sum of currents entering any junction in a circuit must equal the sum of currents leaving that junction.

  20. 28.3 • Loop Rule- The sum of the potential differences across all elements around any closed circuit loop must be zero.

  21. 28.3 • When “traveling a loop” the potential difference for resistor elements is –IR with the current, +IR against the current.

  22. 28.3 • When “traveling a loop” the potential difference for emf sources is +ε when moving through – to +, -ε when moving from + to –.

  23. 28.3 • General Rules • Draw a circuit diagram and label the current with direction in each branch. • An Equation is needed for each unknown quantity, usually one for each unknown current. • Series Resistors have the same current. • If a current is solved to be negative, the magnitude is correct, but direction is opposite. • Charge capacitors act as open branches and current = 0.

  24. 28.3 • Quick Quiz p. 871 • Examples 28.8-28.10

  25. 28.4 RC Circuits • One type of DC circuit includes both Resistors and Capacitors. • An RC circuit will have a current that varies over time.

  26. 28.4 • When the switch closes, current will flow charging the capacitor. • As the capacitor reaches maximum charge, the current approaches zero. • At any time, the Kirchoff’s Loop rule applies as follows

  27. 28.4 • The instant the switch is closed, the charge q =0, and the initial current at t = 0 is • As q increases, I decreases until the capacitor is at its maximum charge and I = 0.

  28. 28.4 • To develop an expression to analyze the circuit as a function of time, we will begin with an expression for instantaneous currrent (I = dq/dt).

  29. 28.4 • We then find a common denominator • When then combine like terms.

  30. 28.4 • We then integrate both sides. • Remember that q = 0 at t = zero.

  31. 28.4 • Solving for q(t) • RC is the time constant, τ, to reach 63.2% of Q

  32. 28.4 • We can differentiate this expression with respect to time to get the current expression.

  33. 28.4 • Discharging the Capacitor • If we remove the battery and discharge the stored energy through a resistor.

  34. 28.4 • Energy Stored in the Capacitor • We know • So for a charging RC circuit • For a discharging RC circuit

  35. 28.4 • Quick Quizzes p 876-77 • Examples 28.11-28.14

  36. 28.5 Electrical Meters28.6 Household Safety • Read 879-882 • Electrical Meters • Galvanometer • Ammeter • Voltmeter • Household Safety • Typical Wiring (Live/Neutral) • Shocking/Fatal Currents • 3rd Ground Wire • GFI’s

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