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**Current, Resistance and Power**

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Battery + - Negative Electrode Positive Electrode electrolyte

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Battery + - Negative Electrode Positive Electrode electrolyte

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**Current Simple flow of charge I (Note Convention) - MKS unit - Ampere**

See Active Figure 27.09 - I (Note Convention) MKS unit - Ampere Current

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**Current Charge carriers + A**

n - concentration of charges per unit volume vd – drift velocity A – cross sectional area of conducting wire q – charges carried by each particle

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**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

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**Volume of passing charges**

+ + + A + + +

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+ + + + + +

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**Current Density and Ohm’s Law**

Current per unit Area

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**Current Density and Ohm’s Law**

s - conductivity

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A more familiar form

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**Resistivity where Volt/amp= W - MKS Unit Resistance Ohm’s Law:**

Macroscopic form where Volt/amp= W - MKS Unit Resistance

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Note Dependencies If you double the area (ie. Adding an addition wire) the effective resistance halves If you add the wire to the length the effective resistance doubles The 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

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**Ohmic (or linear) device**

Slope = 1/R I Non-Ohmic (or nonlinear) device V

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**Microscopic View of Conductor**

copper Electron Charge Cross sectional area acceleration Time between collisions Independent of Electric Field: Ohmic But can depend on conditions which effect t, such as temperature See Active Figure 27.09

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**Resistivity vs. Temperature**

r(T) – characteristic of material T r r T semi-conductors insulators metallic

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**– thermal coefficient of resistivity**

r0 – resistivity at T0 – thermal coefficient of resistivity

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Superconductors Many materials will below a specific characteristic temperature, Tc, have a pronounced decrease in resistivity.

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**Power Battery – “works” to push current through circuit**

Powersource = VI V – Potential Source I – Current sent from source through circuit I V

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**Thermal energy dissipated through resistors**

Voltage drop across resistor Rate of Thermal Energy dissipation through Resistor

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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?

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**- actual potential difference between electrodes of battery (EMF)**

Battery (Source) e - actual potential difference between electrodes of battery (EMF) r – internal resistance of battery

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r Battery (Source) e I R By 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

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**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).

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V = e - Ir Battery voltage terminal to terminal r e I R Jumping 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

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To find the current… r e I R Kirchoff’s Voltage Loop

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**Resistors in Series and Parallel: Equivalent Resistance**

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Resistors in Series R1 e R3 I R2 I

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Resistors in Series e I Rseries

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**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.

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Resistors in Parallel I e R1 R2 R3 I

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Resistors in Parallel e I R3 R2 R1 I2 I1 I3

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Resistors in Parallel e I R3 R2 R1 I2 I1 I3

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Resistors in Parallel e I R3 R2 R1 I2 I1 I3

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Resistors in Parallel e I R3 R2 R1 I2 I1 I3

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Resistors in Parallel I e I Rparallel I

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Resistors in Parallel

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**Break circuit down into series and parallel resistors**

Solve for the currents going through each of the resistors by circuit reduction (equivalent resistance) 42 V 2 W 12 W 4 W 1 W Break circuit down into series and parallel resistors

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**Currents in the various branches**

2 W 12 W 4 W 1 W I1 I2 I

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42 V 2 W 12 W 4 W 1 W I1 I2 I Find equivalent resistance for the Series Resistors

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**Find Equivalent Parallel Resistance**

12 W I I2 42 V 3 W 6 W I1 Find Equivalent Parallel Resistance

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**Find Equivalent Series Resistance**

12 W I 42 V 2 W Find Equivalent Series Resistance

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**Find Equivalent Series Resistance**

14 W I Find Equivalent Series Resistance

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42 V 14 W I

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12 W I I2 1 W 2 W 42 V I1 2 W 4 W

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42 V 2 W 12 W 4 W 1 W I1 I2 I

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Kirchoff’s Analysis Solve simultaneously for the unknown currents

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