P. Piot, PHYS 375 –Spring 2008PHYS 375: Introduction• Some general remarks• Note on labs• Today’s lecture:– Storing electric energy– Voltage, Current, Power– Conductivity, Ohm’s law–Resistor– Kirchoff’s laws– Series and parallel circuits– Thevenin & Northon equivalent circuitsP. Piot, PHYS 375 –Spring 2008Introduction• Instructors:– Philippe Piot (NIU/FNAL/ANL) at NIU on Mondays this semester; lectures, labs, and homeworks– Nikolai Vinogradov at NIU most of the time will take care of the labs execution and grading. • Book (required): – An Introduction to Modern Electronics by William L. Faissler. • Course web page see:http://nicadd.niu.edu/~piot/phys_375/• Grading: labs: 30 %, homework: 30 %, midterm: 20 %, final 20 %P. Piot, PHYS 375 –Spring 2008LAB: Octave http://www.gnu.org/software/octave/• Example how to make a plot:> v=[0, 3, 5, 10, 40, 23]> i=[0, 4, 2, 1, 0.1 , 0.01]> plot (i,v)• For log or log-log plot> semilogx(i,v)> semilogy(i,v)> loglog(i,v) • Other features:– Can work with complex number– Polynominal fits,…– Can numerically solve ODE –….P. Piot, PHYS 375 –Spring 2008LAB: Error bars• When providing some experimentally measured value you will need to provide the uncertainty or errorbar on this value•If• Then the uncertainty on C is ∆C:•If• Then the uncertainty on C is ∆C:• for more complex equation take the log and differentiate…BAC +=|||||| BAC∆+∆=∆ABC =|||||| BAABC∆+∆=∆P. Piot, PHYS 375 –Spring 2008Storing energy: static electricity example• Rubbing a wool cloth on a piece of wax create a charge unbalance– Wax has an excess of electrons– Wool has a deficit of electrons• Wax and wool are attracted via an Electric force that tries to bring back the electron at their original position around the nuclei• If a wire is contacted to the wax and wool cloth electron will flow from wax to wool cloth• By rubbing the two elements we stored energy in the system {Wax + Wool cloth} this is potential (electric) energyP. Piot, PHYS 375 –Spring 2008Storing energy: gravity example• A similar example of energy storing system is a water reservoir and pond• Pumping the water from the pond into a reservoir provide the necessary work needed to stored energy (here “gravitational”potential energy, U=mgh) – this is analogous to rubbing the piece of wax against the wool cloth• Turning off the pump and letting the water drain back to the pond is analogous to contacting a write on the wax and cloth to let the electron flowing back to their initial stateRubbing wax andwool clothtogetherP. Piot, PHYS 375 –Spring 2008Voltage• The potential energy stored in a system is capable of provoking electron to flow in a conductor.• Potential electric energy is U=eV where V is the voltage, and e the electron charge ABBAldEV Φ−Φ==∫vr.eVldEeldFW ===∫∫rvrv..• The voltage is the required work top move a charge from a point to another point dtdNedtdQI =≡• The flow of electron is called current: it is the charge flow per unit of time:P. Piot, PHYS 375 –Spring 2008Storing electric energy: battery• In essence the example of {wax + wool cloth} system can be seen as a battery.• Practically battery are mainly based on chemical reaction (e.g. a series of plate bathing in a liquid or semi-solid medium)Symbol for batteryP. Piot, PHYS 375 –Spring 2008Current versus Voltage source• In practical situation there are – Voltage sources, and – Current sources.• Voltage sources: ideally provide a voltage valuefor any load • Current sources: ideally provide a current valuefor any loadP. Piot, PHYS 375 –Spring 2008• For large time after the electric field has been established thevelocity is constant (steady state) .•So Drude model of a conductor• Model of conduction elaborated by Paul Karl Ludwig Drude (1863-1906)• The equation of motion in a conductor under the influence of an electric field isvmEedtvdmrvrτ−=Motion due to E-fieldDrag force due to scatteringftvvrr→∞→µττmemveEvmeEff≡=⇔−=−10Electron mobilityP. Piot, PHYS 375 –Spring 2008Drude model of a conductor• Solution of previous equation is simplywherein τ is the relaxation time. Here we considered one electron only−=−τtfevtv 1)(• The current associated to a collection of electron with electronic density n (i.e. n is a number of electron per unit of volume) is: • So we have a generally linearvectorial relation between J and E: .EmNenevJfτ2==EEJrrrρσ1≡=conductivityresistivityP. Piot, PHYS 375 –Spring 2008Ohm’s law• J is a current density, the current, I, is the surface integral• many assumption are “buried” in the previous equation: we assume the E-field is constant over the conductor cross-section and length. Lis the considered length within the conductor and A the cross-sectional area. R is the conductor resistance• Ohm’s law generally written asappeared in Die galvanische Kette, mathematisch bearbeitet. Between 1825-27, Georg Simon Ohm (1789-1854), had been studying electrical conduction following as a model Fourier's study of heat conduction. RIV=VRVLASdESdJI1.. ≡===∫∫∫∫σσrrrrGeorg Simon Ohm (1789-1854),P. Piot, PHYS 375 –Spring 2008Some units…• V, the voltage is measured in Volt (Alessandro Volta); symbol is V• I, the current is measured in Ampère (André Ampère); symbol is A• R, the resistance is measured in Ohm (Georg Ohm); symbol isΩAndré Marie Ampère (1775 - 1836)Alessandro Volta (1747-1827)P. Piot, PHYS 375 –Spring 2008Power & alternative expression of Ohm’s law• Another measure of the free electrons activity in a metal is the power. The power is the amount of work done per unit of time • The power is measured in Watt (symbol W)• Using Ohm’s law the power can be expressed as:• So resistance dissipates power (Joule’s heating)VIdteNdVdteNVddtdWP ====)()(James Watt (1736-1819)RVRIP22==Refer to as Joule’s lawJames Precott Joule (1818-1889)P. Piot, PHYS 375 –Spring 2008Resistors• Resistance is useful if its value is controlled• Resistors are special components made for the express purpose of creating a precise quantity of resistance for insertion in an electric circuit. • Typically made of metal write or carbon and engineered to maintain a precise, stable value of resistance over a wide range of environmental conditions. • Resistors