4 Current Simple flow of charge I (Note Convention) - MKS unit - Ampere See Active Figure 27.09-I(Note Convention)MKS unit - AmpereCurrent
5 Current Charge carriers + A n - concentration of charges per unit volumevd – drift velocityA – cross sectional area of conducting wireq – charges carried by each particle
6 The volume contains the passing charges can be found with vd, A and Dt After some time Dt, the particles will pass beyond a particular point on the wire+++A+++The volume contains the passing charges can be found with vd, A and Dt
12 Resistivity where Volt/amp= W - MKS Unit Resistance Ohm’s Law: Macroscopic formwhereVolt/amp= W - MKS UnitResistance
13 Note DependenciesIf you double the area (ie. Adding an addition wire) the effective resistance halvesIf you add the wire to the length the effective resistance doublesThe resistivity is an intrinsic property of the material the resistor is made of. If you change material keeping physical geometry the same, the resistance changes
15 Microscopic View of Conductor copperElectron ChargeCross sectional areaaccelerationTime between collisionsIndependent of Electric Field: OhmicBut can depend on conditions which effect t, such as temperatureSee Active Figure 27.09
16 Resistivity vs. Temperature r(T) – characteristic of materialTrrTsemi-conductorsinsulatorsmetallic
17 – thermal coefficient of resistivity r0 – resistivity at T0– thermal coefficient of resistivity
18 SuperconductorsMany materials will below a specific characteristic temperature, Tc, have a pronounced decrease in resistivity.
19 Power Battery – “works” to push current through circuit Powersource = VIV – Potential SourceI – Current sent from source through circuitIV
20 Thermal energy dissipated through resistors Voltage drop across resistorRate of Thermal Energy dissipation through Resistor
21 Example Problem: Suppose we wanted to design a small heater for your to work before your car warmed up. We want 500Watts using the 12V of your car battery. How much Nichrome wire with a crossectional area of 0.1 cm2 do we need?
22 - actual potential difference between electrodes of battery (EMF) Battery (Source)e- actual potential difference between electrodes of battery (EMF)r – internal resistance of battery
23 rBattery (Source)eIRBy attaching the battery to a circuit including a load resistor R, the current drawn through the battery will effect the actual potential difference in the battery
24 Kirchoff’s Voltage Loop Theorem The algebraic sum of the changes in electric potential encountered in a complete traversal of the circuit must be zero.A circuit is closed path through which current (electrons) may be forced to move through circuit elements (resistors).
25 V = e - IrBattery voltage terminal to terminalreIRJumping from the negative to the positive end of the battery, the potential increases by e, but after going through the resistor, the potential drops by IR
26 To find the current…reIRKirchoff’s Voltage Loop
31 Kirchoff’s Junction Theorem At any junction (point where current can split) the algebraic sum of the currents into and out of the wires of the junction must add to zero.By convention the current into a junction is positive and the current out of a junction is negative.
39 Break circuit down into series and parallel resistors Solve for the currents going through each of the resistors by circuit reduction (equivalent resistance)42 V2 W12 W4 W1 WBreak circuit down into series and parallel resistors
40 Currents in the various branches 2 W12 W4 W1 WI1I2I
41 42 V2 W12 W4 W1 WI1I2IFind equivalent resistance for the Series Resistors