1. 2/7/07184 Lecture 181 PHY 184 Spring 2007 Lecture 18 Title: Resistor Circuits

2. 2/7/07184 Lecture 182AnnouncementsAnnouncements  Midterm 1 will take place in class tomorrow  Chapters 16 - 19 Homework Sets 1 - 4 You may bring one 8.5 x 11 inch sheet of equations, front and back, prepared any way you prefer. Bring a calculator Bring a No. 2 pencil Bring your MSU student ID card  We will post Midterm 1 as Corrections Set 1 after the exam You can re-do all the problems in the Exam You will receive 30% credit for the problems you missed To get credit, you must do all the problems in Corrections Set 1, not just the ones you missed

3. 2/7/07184 Lecture 183 Seating Instructions Thursday Fall Semester 2006 Midterm 1 Section 1 Alphabetical Seating Order  Please seat yourselves alphabetically.  Sit in the row (C, D,…) corresponding to your last name alphabetically.  For example, Bauer would sit in row C, Westfall in row O.  We will pass out the exam by rows. Section 2

4. 2/7/07184 Lecture 184 Review - Temperature Dependence  The temperature dependence of the resistance of metallic conductors is given by R is the resistance at temperature T R 0 is the resistance at temperature T 0  is the temperature coefficient of electric resistivity for the material under consideration

5. 2/7/07184 Lecture 185 Review – Par and Ser Resistors  We can replace n parallel resistors with one equivalent resistor given by  We can replace n series resistors with one equivalent resistor given by

6. 2/7/07184 Lecture 186 Example: Network of Resistors  Consider the network of resistors shown below  Calculate the current flowing in this circuit.

7. 2/7/07184 Lecture 187 Example: Network of Resistors (2)  Ok, let’s look at it. R 3 and R 4 are in series  Now note that R 34 and R 1 are in parallel

8. 2/7/07184 Lecture 188 Example: Network of Resistors (3)  And now R 2, R 5, R 6, and R 134 are in series

9. 2/7/07184 Lecture 189 Clicker Question  Consider the circuit on the right.  Which statement is correct? A) R 2 and R 3 are in parallel B) R 1 and R 3 are in series C) R 1 and R 2 are in parallel D) Several statements above are correct

10. 2/7/07184 Lecture 1810 Clicker Question  Consider the circuit on the right.  Which statement is correct? C) R 1 and R 2 are in parallel R1 and R2 have the same voltage across them. R2 and R3 do not have the same voltage drop, so they cannot be in parallel. R1 and R3 do not have the same current flowing through them, so they cannot be in series.

11. 2/7/07184 Lecture 1811 More resistors …  The figure shows a circuit containing one ideal 12 V battery (no internal resistance) and 4 resistors with R 1 =20 , R 2 =20 , R 3 =30 , and R 4 =8 .  What is the current through the battery? Idea: Find the equivalent resistance and use Ohm’s Law. R 2 and R 3 are in parallel.

12. 2/7/07184 Lecture 1812 More resistors …  R 23 =12   What is the current through the battery? R 1, R 23 and R 4 are in series.

13. 2/7/07184 Lecture 1813 More resistors …  The circuit contains one ideal 12 V battery (no internal resistance) and 4 resistors with R 1 =20 , R 2 =20 , R 3 =30 , and R 4 =8 .  What is the current i 2 through R 2 ? Key Idea 1: R 2 and R 3 are in parallel, so they have the same voltage drop V 2 =V 3 =V 23 Key Idea 2: R 1, R 23 and R 4 are in series so they have the same current V 23 =iR 23 =(0.3 A)(12  )=3.6 V

14. 2/7/07184 Lecture 1814 More resistors …  The figure on the right shows a circuit containing one ideal 12 V battery (no internal resistance) and 4 resistors with R 1 =20 , R 2 =20 , R 3 =30 , and R 4 =8 .  What is the current i 3 through R 3 ? Key Idea: Conservation of charge tells us that the current i going through R 23 must be equal to the sum of the currents through R 2 and R 3.

15. 2/7/07184 Lecture 1815 Light Bulbs in Parallel and in Series +12 V - 12V In parallel: Observation: Take out one bulb, nothing happens to the others Assume: the bulbs are almost identical and have the same resistance

16. 2/7/07184 Lecture 1816 Clicker Question +12 V - 12V In parallel: What voltage drop will be measured across one light bulb? A) 12 V B) 24 V C) 36 V

17. 2/7/07184 Lecture 1817 Clicker Question +12 V - 12V In parallel: What voltage drop will be measured across one light bulb? B) 24 V Since the bulbs are wired in parallel: the voltage drop is the same for all and equal to the voltage supplied by the emf device

18. 2/7/07184 Lecture 1818 Light Bulbs in Parallel and Series +12 V - 12V In series: Observation: Taking one bulb out breaks the circuit. The more bulbs we put in series, the dimmer they get! Assume: the bulbs are almost identical and have the same resistance

19. 2/7/07184 Lecture 1819 Clicker Question +12 V - 12V In series: What voltage drop will be measured across one light bulb? A) 8 V B) 12 V C) 24 V

20. 2/7/07184 Lecture 1820 Clicker Question +12 V - 12V In series: What voltage drop will be measured across one light bulb? A) 8 V In series: V emf =V 1 +V 2 +V 3, all resistances are the same. We measure V emf /3=24/3=8 V across each bulb

21. 2/7/07184 Lecture 1821 Energy and Power in Electric Circuits  Consider a simple circuit in which a source of emf with voltage V causes a current i to flow in a circuit.  The work required to move a differential amount of charge dq around the circuit is equal to the differential electric potential energy dU given by  The definition of current is  So we can rewrite the differential electric potential energy as  The definition of power P is  Pitting it together

22. 2/7/07184 Lecture 1822 Energy and Power  The power dissipated in a circuit or circuit element is given by the product of the current times the voltage.  Using Ohm’s Law we can write equivalent formulations of the power  The unit of power is the watt (W).  Electrical devices are rated by the amount of power they consume in watts.  Electricity bill is based on how many kilowatt-hours of electrical energy you consume.  The energy is converted to heat, motion, light, … with kW h = power times time 1 kW h = 1000 W X 3600 s = 3.6 x 10 6 joules

23. 2/7/07184 Lecture 1823 Temperature Dependence of the Resistance of a Light Bulb  A 100 W light bulb is connected to a source of emf with V emf = 100 V.  When the light bulb is operating, the temperature of its tungsten filament is 2520 °C.  Question:  What is the resistance of the light bulb at room temperature (20 °C)?  Answer:  Power when lighted

24. 2/7/07184 Lecture 1824 Temperature Dependence of the Resistance of a Light Bulb (2)  … so  The temperature dependence of the resistance  … solve for the resistance at room temperature, R 0  Look up the temperature coefficient for tungsten …

25. 2/7/07184 Lecture 1825 Total Energy in a Flashlight Battery  A standard flashlight battery can deliver about 2.0 Wh of energy before it runs down.  If a battery costs US$ 0.80, what is the cost of operating a 100 W lamp for 8.0 hours using standard batteries? Answer: $320