Chapter 18Sources of emfemf and Internal ResistanceMore About Internal ResistanceInternal Resistance and emf, contInternal Resistance and emf, finalResistors in SeriesResistors in Series, contEquivalent Resistance – SeriesEquivalent Resistance – Series: An ExampleResistors in ParallelEquivalent Resistance – Parallel, ExampleEquivalent Resistance – ParallelProblem-Solving Strategy, 1Problem-Solving Strategy, 2Problem-Solving Strategy, 3Problem-Solving Strategy, 4Equivalent Resistance – Complex CircuitGustav KirchhoffKirchhoff’s RulesStatement of Kirchhoff’s RulesMore About the Junction RuleSetting Up Kirchhoff’s RulesMore About the Loop RuleLoop Rule, finalJunction Equations from Kirchhoff’s RulesLoop Equations from Kirchhoff’s RulesProblem-Solving Strategy – Kirchhoff’s RulesRC CircuitsCharging Capacitor in an RC CircuitNotes on Time ConstantDischarging Capacitor in an RC CircuitHousehold CircuitsHousehold Circuits, cont.Electrical SafetyEffects of Various CurrentsGround WireGround Fault Interrupts (GFI)Electrical Signals in NeuronsDiagram of a NeuronChapter 18Direct Current CircuitsSources of emfThe source that maintains the current in a closed circuit is called a source of emfAny devices that increase the potential energy of charges circulating in circuits are sources of emfExamples include batteries and generatorsSI units are VoltsThe emf is the work done per unit chargeemf and Internal ResistanceA real battery has some internal resistanceTherefore, the terminal voltage is not equal to the emfMore About Internal ResistanceThe schematic shows the internal resistance, rThe terminal voltage is ΔV = Vb-VaΔV = ε – IrFor the entire circuit, ε = IR + IrInternal Resistance and emf, contε is equal to the terminal voltage when the current is zeroAlso called the open-circuit voltageR is called the load resistanceThe current depends on both the resistance external to the battery and the internal resistanceInternal Resistance and emf, finalWhen R >> r, r can be ignoredGenerally assumed in problemsPower relationshipI  = I2 R + I2 rWhen R >> r, most of the power delivered by the battery is transferred to the load resistorResistors in SeriesWhen two or more resistors are connected end-to-end, they are said to be in seriesThe current is the same in all resistors because any charge that flows through one resistor flows through the otherThe sum of the potential differences across the resistors is equal to the total potential difference across the combinationResistors in Series, contPotentials addΔV = IR1 + IR2 = I (R1+R2)Consequence of Conservation of EnergyThe equivalent resistance has the effect on the circuit as the original combination of resistorsEquivalent Resistance – SeriesReq = R1 + R2 + R3 + …The equivalent resistance of a series combination of resistors is the algebraic sum of the individual resistances and is always greater than any of the individual resistorsEquivalent Resistance – Series: An ExampleFour resistors are replaced with their equivalent resistanceResistors in ParallelThe potential difference across each resistor is the same because each is connected directly across the battery terminalsThe current, I, that enters a point must be equal to the total current leaving that pointI = I1 + I2The currents are generally not the sameConsequence of Conservation of ChargeEquivalent Resistance – Parallel, ExampleEquivalent resistance replaces the two original resistancesHousehold circuits are wired so the electrical devices are connected in parallelCircuit breakers may be used in series with other circuit elements for safety purposesEquivalent Resistance – ParallelEquivalent ResistanceThe inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistanceThe equivalent is always less than the smallest resistor in the group321eqR1R1R1R1Problem-Solving Strategy, 1Combine all resistors in seriesThey carry the same currentThe potential differences across them are not the sameThe resistors add directly to give the equivalent resistance of the series combination: Req = R1 + R2 + …Problem-Solving Strategy, 2Combine all resistors in parallelThe potential differences across them are the sameThe currents through them are not the sameThe equivalent resistance of a parallel combination is found through reciprocal addition:321eqR1R1R1R1Problem-Solving Strategy, 3A complicated circuit consisting of several resistors and batteries can often be reduced to a simple circuit with only one resistorReplace any resistors in series or in parallel using steps 1 or 2. Sketch the new circuit after these changes have been madeContinue to replace any series or parallel combinations Continue until one equivalent resistance is foundProblem-Solving Strategy, 4If the current in or the potential difference across a resistor in the complicated circuit is to be identified, start with the final circuit found in step 3 and gradually work back through the circuitsUse ΔV = I R and the procedures in steps 1 and 2Equivalent Resistance – Complex CircuitGustav Kirchhoff1824 – 1887Invented spectroscopy with Robert BunsenFormulated rules about radiationKirchhoff’s RulesThere are ways in which resistors can be connected so that the circuits formed cannot be reduced to a single equivalent resistorTwo rules, called Kirchhoff’s Rules can be used insteadStatement of Kirchhoff’s RulesJunction RuleThe sum of the currents entering any junction must equal the sum of the currents leaving that junctionA statement of Conservation of ChargeLoop RuleThe sum of the potential differences across all the elements around any closed circuit loop must be zeroA statement of Conservation of EnergyMore About the Junction RuleI1 = I2 + I3From Conservation of ChargeDiagram b shows a mechanical analogSetting Up Kirchhoff’s RulesAssign symbols and directions to the currents in all branches of the circuitIf a direction is chosen incorrectly, the resulting answer will be negative, but the magnitude will be correctWhen applying the loop rule, choose a direction for transversing the loopRecord voltage drops and rises as they occurMore About the Loop RuleTraveling