From last timeDC circuitsR and C in parallel and seriesKirchhoff’s lawsEMFMore on Capacitors and Capacitance (Human capacitors)Energy stored in CapacitorsCurrentResistanceOhm’s LawToday:This week Honor LectureDetecting the Body’s electrical signal Prof. R. MossDept. of PhysiologyMTE 2: Ch 2103 5:30-7pm on Mar 26 Contact me and Prof. Rzchowskiafter this lecture for Alternate Exams (also by email asap!)3Quick Quiz4€ R =ρLATwo cylindrical conductors are made from the samematerial. They are of equal length but one has twicethe diameter of the other.A. R1 < R2B. R1 = R2C. R1 > R221Ohm’s LawDefine: R = ρL/AResistance in ohms (Ω)Ohm’s law becomes: ΔV = R Iohmic device: relationship current and voltage is linear€ E =ΔVL=ρIAOhm’s Law: J = σ E or E = ρ Jρ = resistivityDependence on Temperatureρ of a conductor varies approximately linearly with T ρo is the resistivity at To = 20° C α = temperature coefficient in SI units of oC-1The higher T the greater atomic vibrations that increases collision probability Similarly: R = Ro[1 + α(T - To)]Lρ = ρ0 +α(Τ−Τ0)T0Tρ0T-T0α x (ρ-ρ0)But other materials…Semiconductors:α is negative ⇒ ρ decreases for increasing TSuperconductorsBelow a certain temperature, TC = critical temperature ρ is zeroOnce a current is set up in a superconductor, it persists without any applied voltage since R = 0€ ρ=ρ01+αΔT( )MercuryResistivityResistivity: ρ = 1 / σ SI units of Ω . mThe resistance depends on resistivity and conductor geometry:Resistors control the current level in circuitsResistors can be composite or wire-woundResistors in SeriesI1 = I2 = IΔV = ΔV1 + ΔV2Req = R1+R2Neglect resistance of wires in circuitsrespect to R resistanceI1I2ΔV1ΔV2€ ΔV = ΔV1+ ΔV2= R1I1+ R2I2= (R1+ R2)I = ReqIRR=2R2 resistors in series:R ∝ LLike summing lengths€ R =ρLAResistors in parallelΔV = ΔV1 = ΔV2I = I 1 + I 2 € I = I1+ I2=ΔV1R1+ΔV2R2=1R1+1R2 ΔV =ΔVReqRRAdd areas€ R =ρLAA A2ACurrent Conservation: 1st Kirchoff’s law11IinIoutIout = IinI1I2I3I1=I2+I3I2I3I1I1+I2=I3Junction Rule: Σ Iin = Σ IoutA statement of Conservation of ChargeCapacitors in seriesΔV1Same charge: Q1 = Q2 = QShare potential difference: ΔV1+ΔV2=ΔVAdd d: € C =ε0AdΔV2ΔV€ ΔV = ΔV1+ ΔV2=Q1C1+Q2C2= Q1C1+1C2 =QCeqelectrons migrate to ++-Capacitors in parallelΔVΔV1=ΔV2ΔVSame voltage: ΔV1=ΔV2=ΔVShare Charge: Q = Q1+Q2Add Areas: C =ε0Ad€ Q = Q1+ Q2= C1ΔV1+ C2ΔV2= (C1+ C2)ΔV = CeqΔVC1Electrical powerPower = rate of energy loss•As a charge ΔQ moves from a to b, the electric potential energy of the system increases by ΔQΔV and the chemical energy in the battery decreases by this same amount•As the charge moves through the resistor (c to d), the system loses this electric potential energy during collisions of the electrons with the atoms of the resistor•This energy is transformed into internal energy in the resistor (vibrational motion of the atoms in the resistor)•Power in units of Watts = J/s14€ P =ΔUΔt=ΔQΔtΔVP = IΔV = RI2=ΔV2RQuick Quiz15How does brightness of bulb B compare to that of A?A. B brighter than AB. B dimmer than AC. Both the same2 Identical Light Bulbs in parallel and seriesA)B)A)B)εεWhich of these statements is true?A) Parallel connection is more luminousB) Series connection is more luminousC) Both connections have the same luminosityEmf and real batteryA battery: device supplying electrical energy to circuitIdeal battery: const. voltage difference between terminals ΔV = ε and I =ε/RReal battery: ΔV = ε - Ir = RI so the battery voltage at its terminals depends on the load resistance R, since ΔV higher for smaller I (higher R) The electromotive force ε: max possible voltage that the battery can provide between its terminals (I=0)ΔV= terminal voltage < εΔVElectrical measurements: AmmeterA multimeter can measure currents (as an ammeter), potential difference (as a voltmeter)Electrical measuring devices must have minimal impact in the circuitIn the absence of the ammeter:I = ε/RIn the presence of the ammeter: I = ε/(R + rA) → ε/Rfor rA →0 the ammeter does not change the behavior of the circuitIAIΔVAΔVR=R1+R2Electrical measurements: VoltmeterIn the absence of the voltmeter: IR = ε/RIn the presence of the voltmeter:I = Iv+IR ΔVV = ΔVR= εIf the resistance of the voltmeter is very large it will not affect the behavior of the circuit€ I =εRV+εRRV→∞ → εRRεVVoltmeterΔVVIVIRIΔVRKirchhoff’s Rules Loop Rule:A statement of Conservation of EnergyRemember that a charge that moves around a closed loop back to the starting point has potential energy difference ΔU=0 (conservative electric force)€ ΔVloop= ΔVk= 0k∑I+-potential increases potential decreases-+I-+potential decreasespotential increases+-What is the current?21€ ε1−ε2− (r1+ R1+ R2+ r2+ R3)I = 012V6V5Ω5Ω25Ω25Ω40Ω€ I=ε1−ε2r1+ R1+ R2+ r2+ R3=6100= 0.06AWhat happens if the polarity of ε2 is reversed? Does I increase or decrease?Kirchoff’s laws application22I1I22 loopsAssume 1 current verse per loopI3€ I1= I3+ I2⇒ I3= I1− I28V + 4V − 4V −1ΩI1− 2ΩI1− 2Ω(I1− I2) = 0−4V − 6ΩI2− 2Ω(I2− I1) = 0An example of DC circuit23Which is the current in the circuit when S1 is open and S2 closed?€ I =εReq= 18112+16 = 4.5A€ I =εReq=182 + 4= 3A€ I =εReq=182 +14= 8 AWhich of this cases for S1 closed and S2 closed?Resistors control the current level in
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