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Introduction to Current In AP C

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Current I = dq/dt I: current in Amperes (A) q: charge in Coulombs (C) t: time in seconds (s)

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Current Density J = I/A J: current density in A/m 2 I: current in Amperes (A) A: area of cross section of wire (m 2 ) I = J A

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Drift Speed of Charge Carriers J = N e v d = {electrons/m 3 }{Coul/electron}{m/s} = C/s/m 2 = A/ m 2 J: current density in Amperes/m 2 v d : drift velocity in m/s n: # charge carriers per unit volume (per m 3 ) e: charge of individual charge carrier (Coulombs)

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In any typical wire e- + + + + E I vdvd J

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On the APC reference table, current density J is not defined, but you have these 2 formulas related to J: J = I/A and V = IR so V = JAR. Now add in resistivity R = ρL/A so V = JA ρL/A V= JρL and V/L = Jρ So does V/L = E inside a wire? Well E = -dV/dL, so E inside wire = ρJ resistivity

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E inside wire = ρJ Find the electric field inside a copper wire of diameter 2 mm carrying a current of 3 milliamps. How would E inside change if…. …….. the wire were half as thick? ……..aluminum were used instead of copper

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Lets consider the number of electrons per unit volume going through a wire Let’s consider the same a copper wire of diameter 2 mm carrying a current of 3 milliamps. If 4 x 10 -3 electrons move through at 1 x10 -5 m/s. Find N. Note: N is # of charges / m 3 while Current density J is # of Amperes / m 2

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Let’s consider the same a copper wire of diameter 2 mm carrying a current of 3 milliamps. If 4 x 10 -3 electrons move through at 1 x10 -5 m/s. Find N. Rearranging we get N = I/ ev d A = 3 x 10 -3 Coul/sec (1.6 x 10 -19 Coul/electron)(1x10 -5 m/s)(π {1x10 -3 m} 2 ) = 5.9 E 26 electrons/cubic meter What would that be in moles of electrons /m3? 991 moles/m3 or 0.000991 moles per cm3

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Ohm’s Law V = IR V : potential drop between two points (Volts, V) I : current (Amps, A) R : resistance (Ohms, )

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Conductors High conductivity Low resisitivity Loose electrons (for most electrical circuits)

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Insulators High resistivity Low conductivity Tightly held electrons (for most electrical circuits)

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Resisitivity, Property of a material which makes it resist the flow of current through it. Ohm-meters ( m)

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Resisitance, R Depends on resistivity and on geometry R = L/A Ohms ( )

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Conductivity, = 1/ The inverse of resisitivity R = L/A =L/σA

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Electrical Power P = IV P: Power in Watts I: Current in Amperes V: Potential Drop in Volts P = i 2 R P = V 2 /R

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Electromotive Force Related to the energy change of charged particles supplied by a cell. Designated as EMF or as . A misnomer: not a force at all!

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Internal Resistance The resistance that is an integral part of a cell. Tends to increase as a cell ages. (refrigeration helps slow this aging down) r

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Internal Resistance When voltage is measured with no current flowing it gives . r V

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Internal Resistance When voltage is measured with current flowing, it gives V T, equal to e – iR. r i V

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Resistors in series R1R1 R2R2 R3R3 R eq = R 1 + R 2 + R 3

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Resistors in parallel R1R1 R2R2 R3R3 1/R eq = 1/R 1 + 1/R 2 + 1/R 3

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Current in a circuit Defined to be opposite direction of the flow of electrons

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Current in a circuit Electrons move in opposite direction I

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AP C Circuit Analysis Unlike the Regents, the AP C exams and college textbooks… 1) define current as the flow of + charge 2) have mixed circuits that with series and parallel elements 3) have capacitors, charging and discharging 4) can have more than one battery. The batteries aren’t necessarily ideal; they can have internal resistance that reduces voltage output. 5) you may need to use a loop rule to figure out voltage drops (Kirchoff's Laws) through simultaneous equations. 6) have coils magnetizing and demagnetizing

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Kirchoff’s 1 st Rule Junction rule. The sum of the currents entering a junction equals the sum of the currents leaving the junction. Conservation of… charge.

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Kirchoff’s 2 nd Rule Loop rule. The net change in electrical potential in going around one complete loop in a circuit is equal to zero. Conservation of energy.

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Using Conventional Current & the Loop Rule

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Internal resistance of real batteries

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Through resistors: Going with the current is like going downhill, negative V, Going against current is like going uphill, + V. Voltage Drops When doing a loop analysis, V =0. Some V are +, some -. Through batteries, going from – to + is an increase, or + V. going from + to - is logically a loss of potential or - V.

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Water analogy

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Applying Kirchhoff’s Laws Goal: Find the three unknown currents. Using Kirchhoff’s Voltage Law First decide which way you think the current is traveling around the loop. It is OK to be incorrect. Using Kirchhoff’s Current Law

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Applying Kirchhoff’s Laws A NEGATIVE current does NOT mean you are wrong. It means you chose your current to be in the wrong direction initially. -0.545 A

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Applying Kirchhoff’s Laws 2.18 A 2.73 A

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From top, looping clockwise: +4V –I 2 3Ω – I 3 5Ω = 0 From middle section, looping clockwise : + I 2 3Ω - I 1 5Ω +8V= 0 Subtract these two equations to eliminate I 1 ; 4V + I 2 11Ω = 0 So I 2 = 4/11 = - 0.36 Amperes Junction rule I 1 + I 2 = I 3 +4V –I 2 3Ω – (I 1 + I 2 )5Ω = 0 +4V –I 2 3Ω – I 1 5Ω - I 2 5Ω = 0 +4V –I 2 8Ω – I 1 5Ω = 0 - 0.36 x 3Ω - I 1 5Ω +8V= 0 So I 1 = +1.38 Amps and I 3 = 1.02 Amps

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Terminology: galvanometers measure small currents (mA), while ammeters measure large currents (whole Amps) Variable Resistors

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BQ V 12 Volts 330 For the drawing shown, calculate a) the current at A b) the total power dissipated by the resistor pair. A

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A current of 4.82 A exists in a 12.4- resistor for 4.60 minutes. a)How much charge and b)How many electrons pass through a cross section of the resistor in this time?

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Friday, February 4 th, 2011 Introducing Current and Direct Current Circuits.

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