PHYS 1442 – Section 004 Lecture #8

1. PHYS 1442 – Section 004 Lecture #8 Monday February 10, 2014 Dr. Andrew Brandt • CH 18 • Electric Power • CH 19 • Resistors • Series and parallel • “Simple” circuits • ***Defer AC to Monday 17th along with short review PHYS 1442-004, Dr. Andrew Brandt

2. Announcements a) HW4 on ch 18 due Tues at 11:30 pm c) HW5 on part of ch 19 due Monday 17th at 5:25 pm (can get a 24 hour extension if in class) d) Test on Weds. Feb. 19th ch 16-18 plus part of ch 19th Mostly multiple guess, bring a scantron, I don’t know how many problems PHYS 1442-004, Dr. Andrew Brandt

3. Why is electric energy useful? • It can be transformed easily into different forms of energy: • Motors, pumps, etc, transform electric energy to mechanical energy • Heaters, dryers, cook-tops, etc., transform electricity to thermal energy • Light bulb filaments transform electric energy to light energy • Only about 10% of the energy turns to light with 90% lost via heat • Typical household light bulb and heating elements have resistance of order few ohms to few hundred of ohms • How does electric energy transform to thermal energy? • Flowing electrons collide with the vibrating atoms of the wire. • In each collision, part of electron’s kinetic energy is transferred to the atom it collides with. • The kinetic energy of wire’s atoms increases, and thus the temperature of the wire increases. • The increased thermal energy can be transferred as heat through conduction and convection to the air in a heater or to food in a pan; it can also be radiated as light. Electric Energy PHYS 1442-004, Dr. Andrew Brandt

4. What is this? Electric Power • How do we find out the power of an electric device? • What is definition of the power? • The rate at which work is done or the energy is transferred • What energy is transferred when charge q moves through a potential difference V? • U=qV; So to move a small amount of charge q in a small amount of time t through a potential difference V, the power P is • Thus, we obtain . • What is the unit? • What kind of quantity is the electrical power? • Scalar • P=IV can apply to any device, while the formulae involving resistance only applies to Ohmic resistors. In terms of resistance Watts = J/s PHYS 1442-004, Dr. Andrew Brandt

5. Example Headlights: Calculate the resistance of a 40-W automobile headlight designed for a 12V battery. Since the power is 40W and the voltage is 12V, we use the formula with V and R. Solve for R PHYS 1442-004, Dr. Andrew Brandt

6. Power in Household Circuits • Household devices usually have small resistance • But since they draw current, if it become large enough, wires can heat up (overload) and cause a fire • Why is using thicker wires safer? • Thicker wires have less resistance, lower heat • How do we prevent this? • Put in a switch that disconnects the circuit when overloaded • Fuse or circuit breakers • They open up the circuit when the current exceeds a certain value Overload PHYS 1442-004, Dr. Andrew Brandt

7. Example Will a 30A fuse blow? Determine the total current drawn by all the devices in the circuit in the figure. The total current is the sum of current drawn by the individual devices. Solve for I Bulb Heater Stereo Dryer Total current What is the total power? Max power? PHYS 1442-004, Dr. Andrew Brandt

8. EMF and Terminal Voltage • What do we need to have current in an electric circuit? • A device that provides a potential difference, such as battery or generator • typically it converts some type of energy into electric energy • These devices are called sources of electromotive force (emf) • This does NOT refer to a real “force”. • The potential difference between terminals of the source, when no current flows to an external circuit, is called the emf () of the source. • A battery itself has some internal resistance (r ) due to the flow of charges in the electrolyte • Why do headlights dim when you start the car? • The starter needs a large amount of current but the battery cannot provide charge fast enough to supply current to both the starter and the headlights PHYS 1442-004, Dr. Andrew Brandt

9. EMF and Terminal Voltage • So the terminal voltage difference is Vab=Va-Vb. • When no current is drawn from the battery, the terminal voltage equals the emf which is determined by the chemical reaction; Vab= . • However when the current I flows from the battery, there is an internal drop in voltage which is equal to Ir. Thus the actual delivered terminal voltage is • Since the internal resistance is inside the battery, we cannot separate the two. PHYS 1442-004, Dr. Andrew Brandt

10. Resistors in Series • Resistors are in series when two or more of them are connected end to end • These resistors represent simple electrical devices in a circuit, such as light bulbs, heaters, dryers, etc. • What is common in a circuit connected in series? • the current is the same through all the elements in series • Potential difference across each element in the circuit is: • V1=IR1, V2=IR2 and V3=IR3 • Since the total potential difference is V, we obtain • V=IReq=V1+V2+V3=I(R1+R2+R3) • Thus, Req=R1+R2+R3 Resistors in series When resistors are connected in series, the total resistance increases and the current through the circuit decreases compared to a single resistor. PHYS 1442-004, Dr. Andrew Brandt

11. Energy Losses in Resistors • Why is it true that V=V1+V2+V3? • What is the potential energy loss when charge q passes through the resistor R1, R2 and R3 • DU1=qV1, DU2=qV2, DU3=qV3 • Since the total energy loss should be the same as the energy provided to the system by the battery , we obtain • DU=qV=DU1+DU2+DU3=q(V1+V2+V3) • Thus, V=V1+V2+V3 PHYS 1442-004, Dr. Andrew Brandt

12. What is this? Battery with internal resistance. A 65.0-W resistor is connected to the terminals of a battery whose emf is 12.0V and whose internal resistance is 0.5-W. Calculate (a) the current in the circuit, (b) the terminal voltage of the battery, Vab, and (c) the power dissipated in the resistor R and in the battery’s internal resistor. Example (a) Since We obtain Solve for I A battery or a source of emf. (b) The terminal voltage Vab is (c) The power dissipated in R and r are PHYS 1442-004, Dr. Andrew Brandt

13. Resistors in Parallel • Resistors are in parallel when two or more resistors are connected in separate branches • Most house and building wirings are arranged this way. • What is common in a circuit connected in parallel? • The voltage is the same across all the resistors. • The total current that leaves the battery, is however, split. • The current that passes through every element is • I1=V/R1, I2=V/R2, I3=V/R3 • Since the total current is I, we obtain • I=V/Req=I1+I2+I3=V(1/R1+1/R2+1/R3) • Thus, 1/Req=1/R1+1/R2+1/R3 Resistors in parallel When resistors are connected in parallel, the total resistance decreases and the current through the circuit increases compared to a single resistor. PHYS 1442-004, Dr. Andrew Brandt

14. Resistor and Capacitor Arrangements • Parallel Capacitor arrangements • Series Resistor arrangements • Series Capacitor arrangements • Parallel Resistor arrangements PHYS 1442-004, Dr. Andrew Brandt

15. Example Series or parallel? (a) The light bulbs in the figure are identical and have identical resistance R. Which configuration produces more light? (b) Which way do you think the headlights of a car are wired? (a) What are the equivalent resistances for the two cases? Series Parallel So The bulbs get brighter when the total power transformed is larger. series parallel So parallel circuit provides brighter lighting. (b) Car’s headlights are in parallel to provide brighter light and also to prevent both lights going out at the same time when one burns out. So what is bad about parallel circuits? Uses more energy in a given time. PHYS 1442-004, Dr. Andrew Brandt

16. Current in one branch. What is the current flowing through the 500-W resistor in the figure? Example We need to find the total current. What do we need to find first? To do that we need to compute the equivalent resistance. Req of the small parallel branch is: Req of the circuit is: Thus the total current in the circuit is The voltage drop across the parallel branch is The current flowing across 500-W resistor is therefore What is the current flowing in the 700-W resister? PHYS 1442-004, Dr. Andrew Brandt What is the current flowing in the 400-W resister?

17. Resistors in Series and in Parallel Conceptual Example: An illuminating surprise. A 100-W, 120-V light bulb and a 60-W, 120-V light bulb are connected in two different ways as shown. In each case, which bulb glows more brightly? Ignore change of filament resistance with current (and temperature). Solution: a.) Each bulb sees the full 120V drop, as they are designed to do, so the 100-W bulb is brighter. b.) P = V2/R, so at constant voltage the bulb dissipating more power will have lower resistance. In series, then, the 60-W bulb – whose resistance is higher – will be brighter. (More of the voltage will drop across it than across the 100-W bulb).

18. Resistors in Series and in Parallel Conceptual Example: Bulb brightness in a circuit. The circuit shown has three identical light bulbs, each of resistance R. (a) When switch S is closed, how will the brightness of bulbs A and B compare with that of bulb C? (b) What happens when switch S is opened? Use a minimum of mathematics in your answers. Solution: a. When S is closed, the bulbs in parallel have half the resistance of the series bulb. Therefore, the voltage drop across them is smaller. Bulbs A and B will be equally bright, but much dimmer than C. b. With switch S open, no current flows through A, so it is dark. B and C are now equally bright, and each has half the voltage across it, so C is somewhat dimmer than it was with the switch closed, and B is brighter.