Lecture 11. Power in Electric Circuits, Kirchhoff s Rules

Lecture 11. Power in Electric Circuits, Kirchhoff s Rules Outline: Energy and power in electric circuits. Voltage and Current Sources. Kirchhoff s Rules. Lecture 10: Connection of resistors in parallel and in series. Batteries: the potential energy of charge carriers is increased by nonelectrostatic (non-conservative) forces. Non-ideal batteries: internal resistance. Potential distribution around a complete circuit. 1

Voltage Source The goal: to provide output voltage that is independent of the load resistance. An ideal voltage source: A. has zero internal resistance ( zero means that << all possible values of load ). B. has infinite internal resistance ( infinite means that >> all possible values of load ). 2

Current Source The goal: to provide output current that is independent of the load resistance. An ideal current source: A. has zero internal resistance ( zero means that << all possible values of load ). B. has infinite internal resistance ( infinite means that >> all possible values of load ). 3

Problem Resistive load: What is the maximum power one can get (dissipate in the load) from a given (, ) battery? 1 2 0 2 0 @ / 1/ current source R<<r voltage source R>>r The wall outlet 120V can be considered as a voltage source the internal resistance is smaller than all typical loads. 4

Light Bulbs The incandescent light bulb: a resistor, being heated by current, emits el.-mag. radiation in the visible wavelength range. voltage source r<<r 1/ is fixed& The larger the power, the smaller the resistance ( is greater than the internal resistance of the voltage source). Bulbs are rated by power. Resistance of a 60W bulb designed for 120V (neglectthe fact that thisrating isforthe AC(notDC)current): 120 60 240Ω Note that a light bulb that is rated at 60Wactually produces only about 3 W of visible light Demonstration 5

Iclicker Question A 60-W light bulb, a 120-W light bulb, and a 240-W light bulb are connected in parallel as shown. Which bulb glows the brightest? 60 W a 120 W b A. the 60-W light bulb B. the 120-W light bulb C. the 240-W light bulb D. All three light bulbs glow with equal brightness. 240 W 6

Iclicker Question A 60-W light bulb, a 120-W light bulb, and a 240-W light bulb are connected in series as shown. Which bulb glows the brightest? 60 W a 120 W A. the 60-W light bulb B. the 120-W light bulb C. the 240-W light bulb D. All three light bulbs glow with equal brightness. 240 W b 8

Iclicker Question Three identical light bulbs are connected to a battery as shown. Which bulb is brightest? A. light bulb A B. light bulb B C. light bulb C D. both light bulbs Band C (both are equally bright and are brighter than light bulb A.) E. All bulbs are equally bright. 10

Kirchhoff s Junction Rule Junction Rule (for currents): charge conservation ' ( ( 0 Currents flowing in + Currents flowing out - 12

Kirchhoff s Loop Rule ) Loop Rule (energy conservation): battery load ' ( ( ' ( ( 0 for any closed loop ' ( ( 0 if we neglect the difference between s and s, and accept the sign conventions. 13

+ +. - +, * + + battery load ) 0 +, -

Example We don t need to know a priori the actual direction of the current: if we get the negative value ofi, that would mean that the current flows in the direction opposite to the direction of travel. ' ( ( ' ( ( 0 4 12 7Ω 2Ω 3Ω 4Ω 0 8 16Ω 0.54 15

Example (cont d) V 4Ω 4V 7Ω 12V 2Ω 3Ω a reference voltage =0 16

Iclicker Question 17

Iclicker Question 44 2Ω 34 4Ω 0 20 18

6 Ω 3 Ω 3 Ω 3 Ω 6 Ω More Examples Problem 26.77: (a) what is the potential difference V ab when the switch is open? (b) What is the current through the switch when the switch is closed? (c) What is the equivalent resistance when the switch is closed? (a) 36 9Ω 44 36 6Ω 44 12 36 3Ω 44 24 12 24 12 19

6 Ω 3 Ω 3 Ω 3 Ω 6 Ω (b) More Examples (cont d) Problem 26.77: (b) What is the current through the switch when the switch is closed? Choose (arbitrary) directions of currents and travel along the loops. Note that the current rule has been taken care of. 1 2 loop 1: 36 6, 3, 0 loop 2: 6, 3 3 0 loop 3: 3, 6 3 0 2, (from Eq.2) 3 3, 12 6 0 (from Eq.3) 3, 12 24, 6 0 3 2, 36 6, 3, 3 2, 36 10.5, 0, 36 10.5 3 2, 2, 0.5, 18 10.5 1.71 - means that our initial direction of I 3 has to be reversed. 20

6 Ω 3 Ω 3 Ω 3 Ω 6 Ω More Examples (cont d) Problem 26.77: (a) what is the potential difference V ab when the switch is open? (b) What is the current through the switch when the switch is closed? (c) What is the equivalent resistance when the switch is closed? (c) 78 1 2, 3, 36 10.5 3 2, : 8.64 9 78 36 8.64 4.2Ω 21

Conclusion Resistors in Series and Parallel Voltmeters and Ammeters Kirchhoff s Rules Next time: Lecture 12: RC circuits 26.4 22

Iclicker Question A 60-W light bulb, a 120-W light bulb, and a 240-W light bulb are connected in series as shown. Across which bulb is there the greatest voltage drop? 60 W a 120 W A. the 60-W light bulb B. the 120-W light bulb C. the 240-W light bulb D. All three light bulbs have the same voltage drop. 240 W b 23

* V * ;< * V * ;< Appendix 1: Voltmeters The goal: to measure the voltage difference across an element (ideally, without affecting the circuit due to the voltmeter connection). An ideal voltmeter: A. has * ;< = and should be connected in parallel with the circuit element being measured. B. has * ;< = and should be connected in series with the circuit element being measured. C. has * ;< and should be connected in parallel with the circuit element being measured. D. has * ;< and should be connected in series with the circuit element being measured. Voltmeter: high internal resistance 25

I * ;< * Appendix 2: Ammeters The goal: to measure the current in a circuit element (ideally, without affecting the current due to the ammeter connection). An ideal ammeter: A. has * ;< = and should be connected in parallel with the circuit element being measured. * I * ;< B. has * ;< = and should be connected in series with the circuit element being measured. C. has * ;< and should be connected in parallel with the circuit element being measured. D. has * ;< and should be connected in series with the circuit element being measured. Ammeter: low internal resistance 26

Appendix 3: Built-in Battery Tester Bi-layer structure: the thermochromic (non-conductive) ink deposited on top of the conductive ink. 78 1, 1 1?,,,, 78 78 78,, T of the thermochromic ink is proportional to P/area: (e.g., is ~2 times smaller than,, and its area is 2 times greater), 4, : 4 : 4 4: 2: 1 27

, V 12Ω A 63V 75V 12Ω 14 15Ω