ESE 271 / Spring 2013 / Lecture 2 Last time we learned Passive sign convention Circuit element absorbs power –acts like a ldload Circuit element delivers power –acts like a generator Energy delivered to circuit element by time t Passive circuit elements: Active circuit elements: Example of active circuit elements: ideal independent voltage and current sources 1 ESE 271 / Spring 2013 / Lecture 2 Last time we discussed Example We will be working with lumped‐parameter model circuits (energy is lumped within circuit elements) 2 ESE 271 / Spring 2013 / Lecture 2 Kirchhoff’s Current Law (KCL) Node can not accumulate any charge, hence current entering the node should be equal to the current leaving the node. Example 3 ESE 271 / Spring 2013 / Lecture 2 Kirchhoff’s Voltage Law (KVL) Sum of voltage drops around any closed loop is zero. Example Sum of voltage drops = Sum of voltage rises 4 ESE 271 / Spring 2013 / Lecture 2 Example KCL at node A KCL at node B KVL around loop 5 ESE 271 / Spring 2013 / Lecture 2 Current in circuit element Let’s find the velocity of electrons moving in constant electric field ‐ Newton’s equation of motion It follows from this analysis that the velocity of electrons and, hence, electric current should increase in time when voltage drop (i.e. electric field) remains constant. This conclusion is not supported by experiment. What is wrong in our analysis? 6 ESE 271 / Spring 2013 / Lecture 2 Ohm’s Law Drift velocity Average time between collisions Drift current didensity: Conductance Conductivity Drift current: Ohm’s law: ‐ Resistance 7 ESE 271 / Spring 2013 / Lecture 2 Resistor Resistivity Passive sign convention Power delivered to resistor: Energy delivered to ideal resistor is being dissipated immediately and gets converted into heat. No energy is stored. (collision of moving electrons with imperfections is friction) 8 ESE 271 / Spring 2013 / Lecture 2 Example 9 ESE 271 / Spring 2013 / Lecture 2 Power rating Real resistors can not dissipate more than certain amount of power without additional heatsink. The power rating limits the maximum values of the current that can be sent through the resistor and maximum value of the voltage that can be applied. 10 ESE 271 / Spring 2013 / Lecture 2 Series connection of resistors KVL: KCL: current is the same in all elements 11 ESE 271 / Spring 2013 / Lecture 2 Voltage divider 12 ESE 271 / Spring 2013 / Lecture 2 Example 13 ESE 271 / Spring 2013 / Lecture 2 Series connection of voltage sources KVL: Equivalent voltage source 14 ESE 271 / Spring 2013 / Lecture 2 Series connection of ideal current sources What values of are physically possible? 15 ESE 271 / Spring 2013 / Lecture 2 Example KCL: KVL: KCL: 16 ESE 271 / Spring 2013 / Lecture 2 Parallel connection of resistors KCL at node 1: 17 ESE 271 / Spring 2013 / Lecture 2 Current divider 18 ESE 271 / Spring 2013 / Lecture 2 Parallel connection of current sources KCL: 19 ESE 271 / Spring 2013 / Lecture 2 Parallel connection of ideal voltage sources What values of are ppyhysicall ypy possible? 20 ESE 271 / Spring 2013 / Lecture 2 Example 21 ESE 271 / Spring 2013 / Lecture 2 Equivalent subcircuits This is equilivalent two‐termilinal subibcircu it. Equivalent means it has the same terminal voltage and current. 22 ESE 271 / Spring 2013 / Lecture 2 Equivalent subcircuits –another example This is equivalent two‐terminal subcircuit. 23.