# Chapter 19 DC Circuits

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1 Lecture PowerPoints Chapter 19 Physics: Principles with Applications, 6 th edition Giancoli Chapter 19 DC Circuits 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Units of Chapter 19 EMF and Terminal Voltage Resistors in Series and in Parallel Kirchhoff s Rules EMFs in Series and in Parallel; Charging a Battery Circuits Containing Capacitors in Series and in Parallel Units of Chapter 19 RC Circuits Resistor and Capacitor in Series Electric Hazards Ammeters and Voltmeters 19.1 EMF and Terminal Voltage Electric circuit needs battery or generator to produce current these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf: 19.1 EMF and Terminal Voltage This resistance behaves as though it were in series with the emf. (19-1) 1

2 19.1 EMF and Terminal Voltage What is the terminal voltage? I = /(R+r) = A A series connection has a single path from the battery, through each circuit element in turn, then back to the battery. V ab = - I r = 11.9 V Batteries loose voltage under load. The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage. From this we get the equivalent resistance (that single resistance that gives the same current in the circuit). (19-3) (19-2) A parallel connection splits the current; the voltage across each resistor is the same: The total current is the sum of the currents across each resistor: 2

3 This gives the reciprocal of the equivalent resistance: (19-4) An analogy using water may be helpful in visualizing parallel circuits: Which configuration produces more light? 19.3 Kirchhoff s Rules Some circuits cannot be broken down into series and parallel connections Kirchhoff s Rules For these circuits we use Kirchhoff s rules. Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it. Loop rule: The sum of the changes in potential around a closed loop is zero Kirchhoff s Rules 3

4 19.3 Kirchhoff s Rules 19.3 Kirchhoff s Rules Problem Solving: Kirchhoff s Rules 1. Label each current. 2. Identify unknowns. 3. Apply junction and loop rules; you will need as many independent equations as there are unknowns. 4. Solve the equations, being careful with signs. Example: I 3 = I 1 + I 2 V ad = V cd + V ac 30 I 1 = I 3 V ad = V af + V da 30 I 1 = 21 I 2 80 I 1 = A I 2 = 2.6 A I 3 = 1.7 A 19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in series in the same direction: total voltage is the sum of the separate voltages 19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in series, opposite direction: total voltage is the difference, but the lowervoltage battery is charged EMFs in Series and in Parallel 19.4 Charging a Battery EMFs in parallel only make sense if the voltages are the same; this arrangement can produce more current than a single emf. 4

5 19.5 Circuits Containing Capacitors in Series and in Parallel Capacitors in parallel have the same voltage across each one: 19.5 Circuits Containing Capacitors in Series and in Parallel In this case, the total capacitance is the sum: (19-5) 19.5 Circuits Containing Capacitors in Series and in Parallel Capacitors in series have the same charge, because regions A and B have zero net charge Circuits Containing Capacitors in Series and in Parallel In this case, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance: V = V 1 + V 2 + V 3 (19-6) 19.6 RC Circuits Resistor and Capacitor in Series If an isolated charged capacitor is connected across a resistor, it discharges: I = dq dt V C = V R dq dt = Q RC 19.6 RC Circuits Resistor and Capacitor in Series When the switch is closed, the capacitor will begin to charge. 5

6 19.6 RC Circuits Resistor and Capacitor in Series The voltage across the capacitor increases with time, as does the charge: 19.7 Electric Hazards Even very small currents 10 to 100 ma can be dangerous, disrupting the nervous system. Larger currents may also cause burns. This curve has a characteristic time constant: Household voltage can be lethal if you are wet and in good contact with the ground. Be careful! A person receiving a shock has become part of a complete circuit Electric Hazards 19.7 Electric Hazards Faulty wiring and improper grounding can be hazardous. Make sure electrical work is done by a professional. Human body: Dry skin 10 6 Ω Wet skin 10 3 Ω One hand in pocket! 19.7 Electric Hazards The safest plugs are those with three prongs; they have a separate ground line. Here is an example of household wiring colors can vary, though! Be sure you know which is the hot wire before you do anything Ammeters and Voltmeters An ammeter measures current; a voltmeter measures voltage. Analog meters are based on galvanometers, digital usually on charging and discharging of capacitors. The current in a circuit passes through the ammeter; the ammeter should have low resistance so as not to affect the current. 6

7 19.8 Ammeters and Voltmeters A voltmeter should not affect the voltage across the circuit element it is measuring; therefore its resistance should be very large Ammeters and Voltmeters An ohmmeter measures resistance; it requires a battery to provide a current 19.8 Ammeters and Voltmeters If the meter has too much or (in this case) too little resistance, it can affect the measurement. Summary of Chapter 19 A source of emf transforms energy from some other form to electrical energy A battery is a source of emf in parallel with an internal resistance Resistors in series: Summary of Chapter 19 Resistors in parallel: Summary of Chapter 19 Capacitors in parallel: Kirchhoff s rules: 1. sum of currents entering a junction equals sum of currents leaving it 2. total potential difference around closed loop is zero Capacitors in series: 7

8 Summary of Chapter 19 RC circuit has a characteristic time constant: To avoid shocks, don t allow your body to become part of a complete circuit Ammeter: measures current Voltmeter: measures voltage 8

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AP* Electric Circuits Free Response Questions 1996 Q4 (15 points) A student is provided with a 12.0-V battery of negligible internal resistance and four resistors with the following resistances: 100 Ω,