1. EEE340Lecture 191 Example 5-1: Vacuum-tube diode Electron cloud where  (y) is negative. The velocity is Newton’s law Hence where (5.9) (5.11) (5.8) y Cathode Anode J E 0 (5.10)

2. EEE340Lecture 192 Therefore On the other hand, from Poisson’s Equation, where Therefore (5.14) (5.12) (5.13)

3. EEE340Lecture 193 Solving (5.14), one obtains Or Child-Langmuir law. The I-V curve can be plotted (non-linear) (5.17)

4. EEE340Lecture 194 5-3: Kirchhoff’s Voltage Law D.C. (per unit length) Skin-effect: ( 5.27) (8.57) Surface-resistance Skin depth (5.27)

5. EEE340Lecture 195 5-4: Kirchhoff’s current law versus the continuity equation. Kirchhoff’s current law: In a steady state The algebraic sum of the currents flowing out of a junction in an electric circuit is zero. Continuity (5.47) ( 5.42)

6. EEE340Lecture 196 Applying the divergence theorem The RHS of (5.42) is Equating the two sides, we have Continuity Equation (5.44)

7. EEE340Lecture 197 In combination with Ohm’s law and Gauss’s law We rewrite (5.44) into Which has a solution (5.50) (5.49)

8. EEE340Lecture 198 We define the relaxation time For copper (5.51)

9. EEE340Lecture 199 5-5: Power Dissipation and Joule’s Law Circuits Power Fields Power density (5.53)