1. CH 20-2

2. Model of a real battery A real battery can be modeled as an ideal battery (i.e. voltage source) and an internal resistance r. The voltage across the terminals is  V =  - Ir With usage, the internal resistance increases and the voltage across the terminals decreases.

3. Example The voltage across a battery is 1.5 V when it is not in a circuit. When connected to a bulb, 0.5 A flows through the battery, and the voltage across the terminals is 1.4 V. What is the internal resistance of the battery?

4. Ideal Voltage Source We will treat all batteries as ideal voltage sources. The voltage across its terminals is constant (and therefore does NOT depend on the current through the voltage source). The current through the voltage source can have any value.

5. Series When elements are connected in series, one element is connected to another element in such a way that there is only one path for current to flow through the elements. The current through each element is the same. I I

6. Total Resistance For two resistors in series, the total resistance is the sum of the resistances. R1R1 R2R2 R eq

7. Example A 1.5 V battery is connected to a 6  resistor and a 10  resistor that are in series. What is the current through the battery? R1R1 R2R2

8. Example A 1.5 V battery is connected to a 6  resistor and a 10  resistor that are in series. What is the voltage across each resistor? R1R1 R2R2

9. Voltage Divider R1R1 R2R2

10. Consider the three resistors and the battery in the circuit shown. Which resistors, if any, are connected in series? A. R 1 and R 2 B. R 1 and R 3 C. R 2 and R 3 D. R 1 and R 2 and R 3 E. No resistors are connected in series. Adapted from David Marx

11. In the circuit shown here, elements _________ are in series. A. E 2 and E 5 B. E 3 and E 4 C. E 4 and E 5 D. none of the above E1E1 E3E3 E5E5 E2E2 E4E4

12. In the circuit shown here, the current will always be equal through elements _________. A. E 1 and E 3 B. E 2 and E 5 C. E 3 and E 4 D. E 4 and E 5 E. none of the above E1E1 E3E3 E5E5 E2E2 E4E4

13. READING QUESTION In the arrangement shown, the resistances R 1, R 2, and R 3 are all different. Here are four proposed statements about this arrangement: 1. The current through each individual resistor is equal to the current through point b. 2. The currents through all the individual resistors add up to the current through point b. 3. The voltage across each individual resistor is equal to the voltage between points a and b. 4. The voltages across all the individual resistors add up to the voltage between points a and b. Which of these statements are correct? A. 1 and 3 B. 1 and 4 C. 2 and 3 D. 2 and 4 R1R1 R2R2 R3R3 b a

14. Parallel Two elements are connected in parallel if their terminals are connected to each other (on both sides). A voltmeter across each element will read the same voltage.

15. Total Resistance For two resistors in parallel, the total resistance is LESS than the sum of the resistances. R eq R1R1 R2R2

16. Example A 1.5 V battery is connected to 6  and 10  resistors that are in parallel. What is the current through the battery? R1R1 R2R2

17. Example A 1.5 V battery is connected to 6  and 10  resistors that are in parallel. What is the current through each resistor? R1R1 R2R2

18. Current Divider R1R1 R2R2

19. Consider the three resistors and the battery in the circuit shown. Which resistors, if any, are connected in parallel? A. R 1 and R 2 B. R 1 and R 3 C. R 2 and R 3 D. R 1 and R 2 and R 3 E. No resistors are connected in parallel. Adapted from David Marx

20. In the circuit shown here, elements _________ are in parallel. A. E 2 and E 3 B. E 1 and E 3 C. E 3 and E 5 D. E 1, E 3, and E 5 E. none of the above E1E1 E3E3 E5E5 E2E2 E4E4 Assume the connecting wires have negligible resistance.

21. In the circuit shown here, elements _________ are in parallel. A. E 2 and E 3 B. E 1 and E 3 C. E 3 and E 5 D. E 1, E 3, and E 5 E. none of the above E1E1 E3E3 E5E5 E2E2 E4E4

22. READING QUESTION In the arrangement shown, the resistances R 1, R 2, and R 3 are all different. Here are four proposed statements about this arrangement: 1. The current through each individual resistor is equal to the current through point b. 2. The currents through all the individual resistors add up to the current through point b. 3. The voltage across each individual resistor is equal to the voltage between points a and b. 4. The voltages across all the individual resistors add up to the voltage between points a and b. Which of these statements are correct? A. 1 and 3 B. 1 and 4 C. 2 and 3 D. 2 and 4 R1R1 R2R2 R3R3 a b

23. In the above circuit, Which of the following correctly compares the currents I A, I B, and I C passing through the three resistors? A. I A > I B > I C B. I C > I B > I A C. I A > I C > I B D. None of the above

24. Power Power is change in energy per second (1 J/s = 1 W). In the case of a battery, the power of the battery is the rate that it supplies electrical energy. In the case of a resistor, the power of the resistor is the rate that it dissipates electrical energy (and converts it to thermal energy and light energy). The brightness of a light bulb depends on its power.

25. A “50 W” bulb and a “100 W” bulb are connected in parallel with a standard 120 volt ac electrical outlet. The brightness of a light bulb is directly related to the power it dissipates. Therefore, the 100 W bulb appears brighter. How does the brightness of the two bulbs compare when these same bulbs are connected in series with the same outlet? A. Both bulbs will be equally bright. B. The “100 W” bulb will be brighter. C. The “50 W” bulb will be brighter. Adapted from David Marx