1. Dr. Jie ZouPHY 13611 Chapter 28 Direct Current Circuits

2. Dr. Jie ZouPHY 13612 Outline Electromotive force (28.1) Resistors in series and parallel (28.2) Examples

3. Dr. Jie ZouPHY 13613 Electromotive force A battery provides a voltage (potential difference) with a fixed polarity, resulting in a direct current in a circuit. is a source of energy for the circuit. is called a source of electromotive force or a source of emf. Direct current: a current that is constant in direction. In general we assume that the connecting wires have no resistance. The emf  of a battery is the maximum possible voltage that the battery can provide between its terminals. An actual circuit

4. Dr. Jie ZouPHY 13614 Internal resistance of a battery Internal resistance r: The resistance to the flow of charge within the battery. Terminal voltage  V: The potential difference across the battery. Load resistance R: The external resistance. Terminal voltage  V =  - Ir. Open-circuit voltage: If I = 0, then  V = . Ideal battery: r = 0 and  V = . Current I =  /(R + r). Total power output of the battery I  = I 2 R + I 2 r. A circuit diagram

5. Dr. Jie ZouPHY 13615 Examples Example 28.1: A battery has an emf of 12.0 V and an internal resistance of 0.05 . Its terminals are connected to a load resistance of 3.00 . (A) Find the current in the circuit and the terminal voltage of the battery. (B) Calculate the power delivered to the load resistor, the power delivered to the internal resistance of the battery, and the power delivered by the battery. Example 28.2 Matching the load: Show that the maximum power delivered to the load resistance R occurs when the load resistance matches the internal resistance (when R = r).

6. Dr. Jie ZouPHY 13616 Resistors in series Properties of series combination: I 1 = I 2 = I  V =  V 1 +  V 2 R eq = R 1 + R 2 +… (R eq is greater than any individual resistance.)

7. Dr. Jie ZouPHY 13617 Resistors in parallel Properties of parallel combination: I = I 1 + I 2  V 1 =  V 2 =  V 1/R eq = 1/R 1 + 1/R 2 +… (R eq is less than the smallest resistance in the group.)

8. Dr. Jie ZouPHY 13618 Examples Quick Quiz 28.4 and 28.7: (a) What happens to the reading on the ammeter when the switch is opened? (b) What happens to the reading on the ammeter when the switch is closed? (a)(b)

9. Dr. Jie ZouPHY 13619 Example 28.4 Find the equivalent resistance Four resistors are connected as shown. (A) Find the equivalent resistance between points a and b. (B) What is the current in each resistor if a potential difference of 42 V is maintained between a and c?

10. Dr. Jie ZouPHY 136110 Example 28.6 Three resistors in parallel Three resistors are connected in parallel as shown. A potential difference of 18.0 V is maintained between points a and b. (A) Find the current in each resistor. (B) Calculate the power delivered to each resistor and the total power delivered to the combination of resistors. (C) Calculate the equivalent resistance of the circuit.

11. Dr. Jie ZouPHY 136111 Real world example: Operation of a three-way light bulb