notes25 2317 - Prof David R Jackson ECE Dept Spring 2011...

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Unformatted text preview: Prof. David R. Jackson ECE Dept. Spring 2011 Notes 25 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism KCL Law KCL Law 1 N n n tot in i i = = = ∑ Wires meet at a “node” i 2 i 3 i N i 4 i 1 KCL Law (cont.) KCL Law (cont.) A C +Q tot in dv i C dt = ground C is the stray capacitance between the “node” and ground. +- v A = surface area of “node.” KCL Law (cont.) KCL Law (cont.) 1) In “steady state” (no time change) 2) As A (area of node) , C tot in dv dt i = = tot in i = tot in dv i C dt = Two cases for which the KCL law is valid: KCL Law (cont.) KCL Law (cont.) In general, the KCL will be accurate if the size of the “node” is small compared with a wavelength λ . node 8 2.99792458 10 c f f λ × = = f λ 60 Hz 5000 [km] 1 kHz 300 [km] 1 MHz 300 [m] 1 GHz 30 [cm] KCL Law (Differential Form) KCL Law (Differential Form) 1 N tot n in n i i = = = ∑ or To obtain the differential form for static (D.C.) currents, start with the definition of divergence: J ∇⋅ = 1 ˆ lim V S J J n dS V ∆ → ∆ ∇ ⋅ ≡ ⋅ ∆ ∫ Ñ ˆ tot out S tot in J ndS i i ∆ ⋅ = = - = ∫ Ñ J ∆ V (valid for D.C. currents) For D.C. : (circuit form) For the right-hand side: Hence Important Current Formulas Important Current Formulas Ohm’s Law J E σ = Charge-Current Formula v J v ρ = (This is an experimental law that was introduced earlier in the semester.)introduced earlier in the semester....
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This note was uploaded on 08/05/2011 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.

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notes25 2317 - Prof David R Jackson ECE Dept Spring 2011...

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