Chapter 27PowerPoint PresentationSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Chapter 27Circuits27.2: Pumping Charges:In order to produce a steady flow of charge through a resistor, one needs a “charge pump,” a device that—by doing work on the charge carriers—maintains a potential difference between a pair of terminals. Such a device is called an emf , or electromotive force.A common emf device is the battery, used to power a wide variety of machines from wristwatches to submarines. The emf device that most influences our daily lives is the electric generator, which, by means of electrical connections (wires) from a generating plant, creates a potential difference in our homes and workplaces. Some other emf devices known are solar cells, fuel cells. An emf device does not have to be an instrument—living systems, ranging from electric eels and human beings to plants, have physiological emf devices.27.4: Calculating the Current in a Single-Loop Circuit:The equation P =i 2R tells us that in a time interval dt an amount of energy given by i2R dt will appear in the resistor, as shown in the figure, as thermal energy. During the same interval, a charge dq =i dt will have moved through battery B, and the work that the battery will have done on this charge, isFrom the principle of conservation of energy, the work done by the (ideal) battery must equal the thermal energy that appears in the resistor:Therefore, the energy per unit charge transferred to the moving charges is equal to the energy per unit charge transferred from them.27.4: Calculating the Current in a Single-Loop Circuit, Potential Method:In the figure, let us start at point a, whose potential is Va, and mentally go clockwise around the circuit until we are back at a, keeping track of potential changes as we move. Our starting point is at the low-potential terminal of the battery. Since the battery is ideal, the potential difference between its terminals is equal to E.As we go along the top wire to the top end of the resistor, there is no potential change because the wire has negligible resistance. When we pass through the resistor, however, the potential decreases by iR. We return to point a by moving along the bottom wire. At point a, the potential is again Va. The initial potential, as modified for potential changes along the way, must be equal to our final potential; that is,27.4: Calculating the Current in a Single-Loop Circuit, Potential Method:For circuits that are more complex than that of the previous figure, two basic rules are usually followed for finding potential differences as we move around a loop:27.5: Other Single-Loop Circuits, Resistances in Series:27.6: Potential between two points:Going clockwise from a: Going counterclockwise from a:27.6: Power, Potential, and Emf:The net rate P of energy transfer from the emf device to the charge carriers is given by:where V is the potential across the terminals of the emf device.But , thereforeBut Pr is the rate of energy transfer to thermal energy within the emf device: Therefore the term iE must be the rate Pemf at which the emf device transfers energy both to the charge carriers and to internal thermal energy.27.7: Multi-loop Circuits:Consider junction d in the circuit. Incoming currents i1 and i3, and it leaves via outgoing current i2. Since there is no variation in the charge at the junction, the total incoming current must equalthe total outgoing current:This rule is often called Kirchhoff’s junction rule (or Kirchhoff’s current law). For the left-hand loop,For the right-hand loop, And for the entire loop,27.7: Multi-loop Circuits, Resistors in Parallel:where V is the potential difference between a and b.From the junction rule,27.7: Multi-loop Circuits:Example, Resistors in Parallel and in Series:Example, Resistors in Parallel and in Series, cont.:Example, Multi-loop circuit and simultaneous loop equations:27.8: Ammeter and Voltmeter:An instrument used to measure currents is called an ammeter. It is essential that the resistance RA of the ammeter be very much smaller than other resistances in the circuit.A meter used to measure potential differences is called a voltmeter. It is essential that the resistance RV of a voltmeter be very much larger than the resistance of any circuit element across which the voltmeter is connected.27.9: RC Circuits, Charging a Capacitor:It turns out that:We know that:27.9: RC Circuits, Time Constant:The product RC is called the capacitive time constant of the circuit and is represented with the symbol :At time t=  =( RC), the charge on the initially uncharged capacitor increases from zero to:During the first time constant  the charge has increased from zero to 63% of its final value CE.27.9: RC Circuits, Discharging a Capacitor:Assume that the capacitor of the figure is fully charged to a potential V0 equal to the emf of the battery E.At a new time t =0, switch S is thrown from a to b so that the capacitor can discharge through resistance R.Fig. 27-16 (b) This shows the decline of the charging current in the circuit. The curves are plotted for R =2000 , C =1 F, and E =10 V; the small triangles represent successive intervals of one time constant .Example, Discharging an RC circuit