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lecture 10

# lecture 10 - Chapter 31 Fundamentals of Circuits 1...

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1 Fundamentals of Circuits Chapter 31

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2 Capacitors in Series + - + - V 1 V + - 2 V 1 C 2 C 1 2 V V V = ∆ + ∆
3 Conductor in Electric Field no electric field E r E r E r equilibrium 0 E = r

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4 Conductor in Electric Field no electric field E r E r conducting wire conducting wire E r ELECTRIC CURRENT
5 Electric Current Electric current is the rate of flow of charge through some region of space The SI unit of current is the ampere (A), 1 A = 1 C / s Assume charges are moving perpendicular to a surface of area A If Q is the amount of charge that passes through A in time t , then the average current is av Q t = I

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6 Ohm’s Law Chapter 28 Chapter 31
7 Current Density I j A = Current density is defined as the current per unit area This expression is valid only if the current density is uniform and A is perpendicular to the direction of the current j has SI units of A/m 2

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8 Ohm’s Law j E σ = Ohm’s Law: Current density is proportional to electric field E r The constant of proportionality, σ , is called the conductivity of the conductor. The conductivity depends only on the material of conductor. 2 n q m τ σ= Simplified model of electron motion in conductor gives - is the material dependent characteristic of conductor.
9 Ohm’s Law Ohm’s law states that for many materials, the ratio of the current density to the electric field is a constant σ that is independent of the electric field producing the current Most metals, but not all, obey Ohm’s law Materials that obey Ohm’s law are said to be ohmic Materials that do not obey Ohm’s law are said to be nonohmic Ohm’s law is not a fundamental law of nature Ohm’s law is an empirical relationship valid only for certain materials j E σ =

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10 Ohm’s Law Conductor E r A B Voltage across the conductor (potential difference between points A and B ) B A V V V El = - = l where electric field is the same along the conductor. Then V E l = I j A = 1 V I E j l A σ = = = j E = l V I RI A = = Another form of the Ohm’s Law
11 Ohm’s Law: Resistance Conductor E r A B l V RI = The voltage applied across the ends of the conductor is proportional to the current through the conductor The constant of proportionality is called the resistance of the conductor resistance SI units of resistance are ohms (Ω) 1 Ω = 1 V / A

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12 Ohm’s Law: Resistance Conductor E r A B l V RI = l R A σ = resistance l R A ρ = Or where is the resistivity – the inverse of the conductivity 1/ = Resistivity has SI units of ohm-meters (Ω m)
13 Resistance: Example Conductor l l

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lecture 10 - Chapter 31 Fundamentals of Circuits 1...

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