Lecture 4 Review: KVL, KCL Circuit analysis examples Series, parallel circuit elements Related educational materials: –Chapter 1.4, 1.5

Review: KVL & KCL KVL: algebraic sum of all voltage differences around any closed loop is zero KCL: algebraic sum of all currents entering a node is zero

Review: Circuit analysis General circuit analysis approach: Assign element voltages, currents according to passive sign convention Apply KVL, KCL, and voltage-current relations as necessary to solve for desired circuit parameters The general idea is to write as many equations as you have unknowns, and solve for the desired unknowns

Circuit analysis – example 1 For the circuit below, determine: v AC, v X, v DE, R X, and the power absorbed by the 2  resistor

Example 1 – continued

Talk about open circuit, short circuit terminology

Circuit analysis tips There are (generally) multiple ways to do a problem Some time spent examining the problem may be productive! Subscript notation on voltages provides desired polarity It may not be necessary to determine all voltages in a loop in order to apply KVL The circuit does not need to be physically closed in order to apply KVL

More circuit analysis tips KVL through a current source is generally not directly helpful Get another equation, but the voltage across a current source is not defined  additional unknown introduced KCL next to a voltage source generally not directly helpful Get another equation, but the voltage across a current source is not defined  introduce an additional unknown

Circuit analysis – example 2 Determine the voltages across both resistors.

Example 2 – continued

Circuit analysis – example 3 We have a “dead” battery, which only provides 2V Second battery used to “charge” the dead battery – what is the current to the dead battery?

Non-ideal voltage source models Add a “source resistance” in series with an ideal voltage source We will define the term series formally later

Non-ideal current source models Add a “source resistance” in parallel with an ideal current source We will define the term parallel formally later

Example 3 – revisited Our battery charging example can now make sense Include internal (source resistances) in our model

Ideal sources can provide infinite power Connect a “load” to an ideal voltage source:

Be sure to discuss previous results relative to open, short-circuit expectations

Non-ideal sources limit power delivery “Loaded” non-ideal voltage source

Validate previous result with open, short- circuit discussion.

Ideal sources can provide infinite power Connect a “load” to an ideal current source:

Be sure to discuss previous results relative to open, short-circuit expectations

Non-ideal sources limit power delivery “Loaded” non-ideal current source

Validate previous results with open vs. short circuit discussion.

When are ideal source models “good enough”? Ideal and non-ideal voltage sources are the “same” if R Load >> R S Ideal and non-ideal current sources are the “same” if R Load << R S

Series and parallel circuit elements Circuit elements are in series if all elements carry the same current KCL at node “a” provides i 1 = i 2

Series and parallel circuit elements Circuit elements are in parallel if all elements have the same voltage difference KVL provides v 1 = v 2

Circuit reduction In some cases, series and parallel combinations of circuit elements can be combined into a single “equivalent” element This process reduces the overall number of unknowns in the circuit, thus simplifying the circuit analysis Fewer elements  fewer related voltages, currents The process is called circuit reduction