1Chapter 23 Revision problemWhile we are waiting, please try problem 14 –“You have a collection of six 1kOhm resistors….”2Electric Circuits• Elements of a circuit• Circuit topology• Kirchhoff’s law for voltage and current• Series and parallel circuit• Household circuits• RC circuits• Nervous system and electricity3Circuits• Combine batteries, resistors, capacitors to make something useful• First circuits to drive something – biophysics• Neurons are circuits in the central nervous system4Elements of a circuit• We will use the following pictograms or symbols• IEEE and ANSI standard• All “ideal” components5Circuit DiagramConvert from pictorial representation to standard symbols6Circuit Topology• Circuits follow simple laws of topology – you can stretch the wires, but you must preserve the number and order of vertices, and order of components• Its normal to re-draw a circuit to make it easier to calculate physical quantities like current and potential difference7Checking UnderstandingThe following circuit has a battery, two capacitors and a resistor. Which of the following circuit diagrams is the best representation of the above circuit?Slide 23-98The following circuit has a battery, two capacitors and a resistor. Which of the following circuit diagrams is the best representation of the above circuit?Slide 23-10Answer9Kirchhoff revisitedWe saw from the last chapter thatThe sum of the currents into a junction is the same as the current flowing out. outinI=I10Kirchhoff’s loop law of electric potential•The energy of an electron in a potential is U=qV•Flowing around a circuit, the electron comes back to the same potential, so it cant gain or lose energy11Kirchhoff’s loop law of electric potential•The net change in the electric potential around any loop must be zeroiiVV 012Multiple batteries in a circuit•Sometimes you see multiple batteries in a circuit.•The larger emf will drive current backwards through the battery with a smaller emf13Series and Parallel CircuitsThere are two types of circuit topology which are useful to identify when calculating current and potential differences14Series CircuitsTwo resistors R1and R2in series have the same affect as a single resistance of RTOTAL21RRRTOTAL15Series CircuitsIn general, the total resistance of a chain of resistors RTOTALis the sum of the individual resistancesjjTOTALRR16Parallel CircuitsTwo resistors R1and R2in parallel have the same affect as a single resistance of RTOTAL21111RRRTOTAL17Parallel CircuitsIn general, the total resistance of a chain of resistors RTOTALcan be calculated from the sum of the reciprocals of the individual resistancesjjTOTALRR1118Measuring Voltage and Current• We use “ideal” instruments for measuring currents – they measure the voltage or current without affecting the quantities we are measuring.• This is quite close to today’s instruments.19Ammeter• Measures current• Used in series• Has zero resistance20Voltmeter• Measures potential difference• Used in parallel• Has infinite resistance21Multimeters• We use multimeters which have an external power supply (battery) and semiconductor amplifiers• Will also measure resistance22Household electricity• Something we should all know about.• DC (Direct Current) is generated by the emf in batteries - used in cars, boats, trailers.• Household electricity is generated by electrical generators which work by producing AC (Alternating Current), but the principles are the same.23Grounding• Grounding (or earthing) is setting one side of the circuit to the same potential as the Earth’s surface• This can make electrical items safer.• Ground is carried by the larger prong on a 3-pin plug24Parallel or Serial ?• All wall outlets are set to carry 120V potential• This is done by using parallel circuits everywhere• Fuses added to protect against large currents25Household energy units• Different units are used for household electricity• We pay for electricity monthly, so we need a bigger unit• A space heater is rated at about 1kW, say we run it for 3 hours a day for a month• Use kilowatt-hours• 1 kW hour = 1000W*3600s = 3.6 MegaJoules26Capacitors in Parallel and Series• Capacitors are used in parallel and series as well.• They look almost, but not quite, exactly opposite of the resistance equations….27Capacitors in ParallelTo calculate total capacitance, need total charge stored321321333222111,,CCCVQQQCVQCVQCVQCtotal28Capacitors in ParallelCapacitance in parallel add togetherjjTOTALCC29Capacitors in Series• To calculate total capacitance, need total charge stored. • Charge must be the same on the 2 capacitors21212221111111,1CCQVVCQVCQVCTOTAL30Capacitors in Series• The total capacitance of capacitors in series can be calculated from the sum of the reciprocals • Charge must be the same on the inside capacitorsjjTOTALCC1131RC Circuits and TimeRC circuits are special circuits which have a characteristic clock built in.The capacitor will gradually discharge32RC CircuitsWe can show that the rate of change of charge is proportional to the remaining charge on the capacitortQRCQtQRIRCQV33RC Circuits• Similarly, the rate of change of voltage is proportional to the voltage• Rate of change of current is proportional to the currenttIRCItVRCV34RC Circuits• It can be shown that the solutions to these equations is an exponential• Where I0and V0are the initial values, and RC is the time constantRCteVtV/0)(RCteItI/0)(35Discharging a capacitor through a resistorRCteVtV/0)(RCteItI/0)(36Charging a capacitor through a resistor)1()(/RCtfinaleVtVRCteItI/0)(37RC Circuits• Easy way to build a clock or oscillator• Make a switch close or open when the potential across a capacitor reaches a certain voltage38Electrical Circuits and Biology• Historically bioelectrics was one of the first uses of electric current to move something –up until then there was electrostatic and magnetic phenomena• Volta and Galvani used electricity to move dead frogs legs.• Cells can drive potassium and sodium ions through membranes with ion pumps –creating an emf39Ion pumps in a cell• The cell attains a 70mV potential across the cell membrane 7nm thick• This is an electric field of 10MV/m40NeuronsNeuron
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