Chapter 18 Direct Current Circuits

General Physics Current, Resistance, and Power Ch 17, Secs 1–4, 6 DC Circuits and RC Circuits Ch 18, Secs 1–3, 5

General Physics Which of the 4 circuits will light the bulb? A 2. B 3. C 4. D

General Physics Sources 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 emfAny devices that increase the potential energy of charges circulating in circuits are sources of emf Examples include batteries and generatorsExamples include batteries and generators  SI units are Volts The emf is the work done per unit chargeThe emf is the work done per unit charge

General Physics emf & Internal Resistance  A real battery has some internal resistance  The schematic shows the internal resistance, r  The terminal voltage is not equal to the emf because voltage drops across the internal resistance  The terminal voltage is: ΔV = V b -V a = ε – Ir Active Figure: A Real BatteryA Real Battery

General Physics Resistors 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 others  The sum of the potential differences across the resistors is equal to the total potential difference across the combination

General Physics Resistors in Series, cont  The current is the same in all resistors I 1 = I 2 = II 1 = I 2 = I  The total potential difference is equal to the sum of the potential differences across the resistors ΔV 1 + ΔV 2 =ΔVΔV 1 + ΔV 2 =ΔV  The resistors can be replaced with one resistor with a resistance of R eq = R 1 + R 2 + …R eq = R 1 + R 2 + …  The equivalent resistor must have exactly the same external effect on the circuit as the original series resistors  The equivalent resistance of a series combination of resistors is greater than any of the individual resistors

General Physics Equivalent Resistance – Series: An Example  Four series resistors are replaced with their equivalent resistance Active Figure: Resistors Connected in SeriesResistors Connected in Series

General Physics Resistors in Parallel  When two or more resistors are connected across each other, they are said to be in parallel  The potential difference across each resistor is the same because each is connected directly across the battery terminals  The sum of the currents through the resistors is equal to the total current through the combination

General Physics Resistors in Parallel, cont  The total current is equal to the sum of the currents in the resistors I 1 + I 2 = II 1 + I 2 = I  The potential difference across the resistors is the same ΔV 1 = ΔV 2 =ΔVΔV 1 = ΔV 2 =ΔV  The resistors can be replaced with one resistor with a resistance of 1/R eq = 1/R 1 + 1/R 2 + …1/R eq = 1/R 1 + 1/R 2 + …  The equivalent resistor must have exactly the same external effect on the circuit as the original parallel resistors  The equivalent resistance of a parallel combination of resistors is less than the smallest of the individual resistors

General Physics Equivalent Resistance – Parallel: An Example  Three parallel resistors are replaced with their equivalent resistance Active Figure: Resistors Connected in ParallelResistors Connected in Parallel

General Physics Problem-Solving Strategy, 1  Combine all resistors in series They carry the same currentThey carry the same current If the resistors are different, the potential differences across them are not the sameIf the resistors are different, the potential differences across them are not the same The resistors add directly to give the equivalent resistance of the series combination:The resistors add directly to give the equivalent resistance of the series combination: R eq = R 1 + R 2 + …

General Physics Problem-Solving Strategy, 2  Combine all resistors in parallel The potential differences across them are the sameThe potential differences across them are the same If the resistors are different, the currents through them are not the sameIf the resistors are different, the currents through them are not the same The equivalent resistance of a parallel combination is found through reciprocal addition:The equivalent resistance of a parallel combination is found through reciprocal addition: 1/R eq = 1/R 1 + 1/R 2 + …

General Physics Problem-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.Replace any resistors in series or in parallel using steps 1 or 2. Sketch the new circuit after these changes have been madeSketch the new circuit after these changes have been made Continue to replace any series or parallel combinationsContinue to replace any series or parallel combinations Continue until one equivalent resistance is foundContinue until one equivalent resistance is found

General Physics Problem-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 2Use ΔV = I R and the procedures in steps 1 and 2

General Physics Equivalent Resistance – Complex Circuit

General Physics How bright will each light be after adding one in parallel? The same as before 2. Brighter than before 3. Dimmer than before

General Physics How bright will each light be after adding one in series? 1. The same as before 2. Brighter than before 3. Dimmer than before

General Physics RC Circuits  A direct current circuit may contain capacitors and resistors – the current will vary with time  When the circuit is completed, the capacitor starts to charge  The capacitor continues to charge until it reaches its maximum charge (Q = Cε)  Once the capacitor is fully charged, the current in the circuit is zero

General Physics Charging Capacitor in an RC Circuit  The charge on the capacitor varies with time q = Q(1 – e -t/RC )q = Q(1 – e -t/RC ) The time constant, =RCThe time constant, =RC  The time constant represents the time required for the charge to increase from zero to 63.2% of its maximum Active Figure: Charging a CapacitorCharging a Capacitor

General Physics Notes on Time Constant  In a circuit with a large time constant, the capacitor charges very slowly  The capacitor charges very quickly if there is a small time constant  After t = 10 , the capacitor is over 99.99% charged

General Physics Discharging Capacitor in an RC Circuit  When a charged capacitor is placed in the circuit, it can be discharged  The charge decreases exponentially q = Qe -t/RCq = Qe -t/RC  At t =  = RC, the charge decreases to of Qmax In other words, in one time constant, the capacitor loses 63.2% of its initial chargeIn other words, in one time constant, the capacitor loses 63.2% of its initial charge Active Figure: Discharging a CapacitorDischarging a Capacitor

General Physics Electrical Safety  Electric shock can result in fatal burns  Electric shock can cause the muscles of vital organs (such as the heart) to malfunction  The degree of damage depends on the magnitude of the currentthe magnitude of the current the length of time it actsthe length of time it acts the part of the body through which it passesthe part of the body through which it passes

General Physics Effects of Various Currents  5 mA or less Can cause a sensation of shockCan cause a sensation of shock Generally little or no damageGenerally little or no damage  10 mA Hand muscles contractHand muscles contract May be unable to let go a of live wireMay be unable to let go a of live wire  100 mA If passes through the body for just a few seconds, can be fatalIf passes through the body for just a few seconds, can be fatal

General Physics Electrical Signals in Neurons  Specialized cells in the body, called neurons, form a complex network that receives, processes, and transmits information from one part of the body to another

General Physics Electrical Signals in Neurons, cont  Three classes of neurons Sensory neuronsSensory neurons  Receive stimuli from sensory organs that monitor the external and internal environment of the body Motor neuronsMotor neurons  Carry messages that control the muscle cells InterneuronsInterneurons  Transmit information from one neuron to another Electron microscope image of neurons in the brain A simple neural circuit