PHYS 0175 1st Edition Lecture 17Outline of Last Lecture II. DielecticsIII. Parallel Plate and seriesIV. Electric CurrentV. Drift speedVI. Current DensityVII. Capacitance with dielecticCurrent LectureVIII. Drift SpeedIX. Current Density and CurrentX. Current through wire with uniform JXI. Current through hollow wireXII. resistanceXIII. resistivityXIV.semiconductorsXV. Dependence on temperatureXVI.Ohm’s LawCurrent LectureII. Drift Speeda. Drift speedb. Based on temperaturec. Presence of E(electric field)d. a=F/m=eE/me. vd=a*tau=J/nei. tau=mean time between collisionsii. n=#charge carriers per unit Vf. more e- bump into eachother, more collisions, slowerg. vd=e*tau*E/mIII. Current Density and Currenta. I=dQ/dt=nqAvdi. Definition of currentb. J=nqvdi. Vector)ii. Unites A/m^2iii. Current is 1D scalar1. I=flux integral for current density2. dA=cross sectional areaIV. Current through wire with uniform Ja. Cross sectional area for dA in integral=pi*r^sb. Since uniform J can take out of integral(a constant)V. Current through hollow wirea. innter and outer radiusb. R is constantc. J=constant=nevdi. J can vary if non uniform materialii. Would be a function of location(radial dist to center)d. Like a shelli. Going from the inner radius edge to the edge of outer radius to find currentii. In this case, J is constant, so can take out as integral b/c constantVI. Resistancea. R=V/I (ohm’s law)b. Measured in ohmsc. R=V/Ad. R depends on:i. Material(through resistivity rho)ii. Geometry: size, shape, placement of contactse. R is how hard to carry charge(work necessary)i. Only for conductorsVII. resistivitya. rhob. rho=E/Jc. non universalohmic conditions(usually metal conductors)d. higher resistivity harder have currentVIII.semiconductorsa. have a gap if too low temperature, will not conduct electricity because too large resistivity(infinity)i. must increase temperature for increase charge carriers(more kinetic energy)ii. able to jump over gapthermal energyiii. metals have no gap, will overlap regardlessIX. Dependence on temperaturea. Resistance and resistivityb. E=pJi. P=rhoii. Rho(T)=rho(initial)*[1+alpha*(T-T(initial))];iii. T=temperatureiv. Alpha=X. Ohm’s Lawa. J(current density) and E have a linear relationshipb. E=pJc. V=RId.
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