Model of a Real Battery: Internal Resistance and Voltage drop

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. R1 R2 Req

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? R1 R2

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? R1 R2

9. Voltage Divider R1 R2

10. Adapted from David Marx Consider the three resistors and the battery in the circuit shown. Which resistors, if any, are connected in series? A.R1 and R2 B.R1 and R3 C.R2 and R3 D.R1 and R2and R3 E. No resistors are connected in series.

11. In the circuit shown here, elements _________ are in series. A. E2 and E5 B. E3 and E4 C. E4 and E5 D. none of the above E1 E3 E4 E2 E5

12. In the circuit shown here, the current will always be equal through elements _________. A. E1 and E3 B. E2 and E5 C. E3 and E4 D. E4 and E5 E. none of the above E1 E3 E4 E2 E5

13. R2 R1 R3 READING QUESTION a b • • In the arrangement shown, the resistances R1, R2, and R3 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

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. R1 Req R2

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? R1 R2

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? R1 R2

18. Current Divider R1 R2

19. Adapted from David Marx Consider the three resistors and the battery in the circuit shown. Which resistors, if any, are connected in parallel? A.R1 and R2 B.R1 and R3 C.R2 and R3 D.R1 and R2and R3 E. No resistors are connected in parallel.

20. In the circuit shown here, elements _________ are in parallel. A. E2 and E3 B. E1 and E3 C. E3 and E5 D. E1, E3, and E5 E. none of the above E1 E3 E4 E2 E5 Assume the connecting wires have negligible resistance.

21. In the circuit shown here, elements _________ are in parallel. A. E2 and E3 B. E1 and E3 C. E3 and E5 D. E1, E3, and E5 E. none of the above E1 E4 E3 E2 E5

22. R1 R2 READING QUESTION a b • • R3 In the arrangement shown, the resistances R1, R2, and R3 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

23. In the above circuit, Which of the following correctly compares the currents IA, IB, and ICpassing through the three resistors? A.IA > IB > IC B.IC > IB > IA C.IA > IC > IB 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