1. Capacitor * What is a capacitor? * Capacitance * Properties Inductor * What is an inductor? * Inductance * Properties Dependent sources * 2 types of independent sources & symbols * 4 types of dependent sources & symbols KVL Lecture 2. More on Circuit Elements &KCL 1

2. 2 Capacitor A passive circuit element that can store charge (energy) –Capacitance (C): describes capacity of storing charge C = q/V Unit: 1 Fara (or F) = 1 Coulomb/Volt Some examples of capacitors Capacitors everywhere

3. 3 Parallel-Plate Capacitor Two conductive parallel plates with a separation usually filled with a certain dielectric material. C =    A/d where     x10 -12 F*m;  is dielectric constant, A is area of the plate and d the separation between the plates. Parallel-plate capacitor

4. 4 Capacitor in Circuits What is V(t 0 )? i(t)i(t) + – v(t) The rest of the circuit Energy stored:

5. 5 Example i(t) + - v(t) The rest of the circuit t i(t) 1A -1A 1s 2s 0.2F v(t)=? w c (t)=?

6. 6 Solution t v(t) 5V 1s 2s t w c (t) 2.5J 1s 2s

7. 7 Inductor A passive circuit element that can store energy in magnetic field –Inductance (L): describes capacity of an element to create a magnetic field flux due to current V = LdI/dt Unit: 1 H = 1 Coulomb/Volt Some examples of capacitors Capacitors everywhere

8. 8 Inductor in Circuits i(t)i(t) + – v(t) The rest of the circuit H Energy stored:

9. 9 Example The current through a 1H inductor is i(t) = 0.45A cos(2  60 t) Find v(t), p(t), and w L (t)

10. 10 Solution p(t)=? w L (t)=? >t=0:0.001:0.1; >i=0.45*cos(2*pi*60*t); >v=-169.7*sin(2*pi*60*t); >plotyy(t,v,t,i) Matlab

11. 11 Independent Sources An independent source (voltage or current) may be DC (constant) or time-varying, but does not depend on other voltages or currents in the circuit +–+– Independent voltage sourceIndependent current source IsIs VsVs 2-types

12. 12 Dependent Sources The dependent source magnitude is a function of another voltage or current in the circuit IsIs VsVs +–+– 6Vx6Vx Voltage-Controlled Voltage Source 6000I x Current-Controlled Voltage Source +–+– 0.006V x Voltage-Controlled Current Source 6Ix6Ix Current-Controlled Current Source 4-types

13. 13 Kirchhoff’s Laws Kirchhoff’s Current Law (KCL) –sum of all currents entering a node is zero –sum of currents entering node is equal to sum of currents leaving node –What is a node? A node is a connection point of three or more circuit elements. Kirchhoff’s Voltage Law (KVL) –sum of voltages around any loop in a circuit is zero –What is a loop or mesh? A loop or mesh is a closed path that does not encircle any other elements or sources.

14. 14 KVL (Kirchhoff’s Voltage Law) v1(t)v1(t) + + – – v2(t)v2(t) v3(t)v3(t) +–+– The sum of voltages around a loop is zero:

15. 15 Applying KVL – the Signs A loop is any closed path through a circuit in which no node is encountered more than once Voltage Polarity Convention –A voltage encountered + to – is positive –A voltage encountered – to + is negative

16. 16 Class Examples Drill Problems 5, 9, 7, 10