Download Kirchhoff's Laws and Circuit Analysis (EC 2) and more Lecture notes Law in PDF only on Docsity! Kirchhoff's Laws and Circuit Analysis (EC 2) • Circuit analysis: solving for I and V at each element • Linear circuits: involve resistors, capacitors, inductors • Initial analysis uses only resistors • Power sources, constant voltage and current • Solved using Kirchhoff's Laws (Current and Voltage) Circuit Nodes and Loops • Node: a point where several wires electrically connect • Symbolized by a dot or circle at the wire crossing • If wires cross without dot, then not connected • Nodes also called junctions • Typically give notes a number or letter • Branches: lines with devices connecting two nodes • Loop: an independent closed path in a circuit • There may be several possible closed paths Kirchhoff's Voltage Law (KVL) • Kirchhoff's Voltage Law (KVL) • Algebraic sum of the voltage drops around any loop or circuit = 0 0 1 =∑ = N j jV where N = number of voltage drops • NOTE: the sign convention • Voltage drops are positive in the direction of the set loop current. • Voltage drops negative when opposite loop current. • Voltage sources positive if current flows out of + side • Voltage sources negative if current flows into + side • A loop is an independent closed path in the circuit. • Define a "loop current" along that path • Real currents may be made up of several loop currents 211 IIIR −= Example Kirchhoff's Voltage Law (KVL) Consider a simple one loop circuit Voltages are number by the element name eg. V1 or VR1 : voltage across R1 Going around loop 1 in the loop direction Recall by the rules: • Voltage drops negative when opposite loop current. • Voltage sources positive if current flows out of + side 01 =−VV s Example Kirchhoff's Voltage Law (KVL) Continued • Thus voltage directions are easily defined here: 01 =−VV s • Why negative V1? Opposes current flow I1 • Since 111 RIV = 011 =− RIV s • Thus this reduces to the Ohms law expression 1 1 R VI s= KVL and KCL for Different Circuits • With multiple voltage sources best to use KVL • Can write KVL equation for each loop • With multiple current sources best to use KCL • Can write KCL equations at each node. • In practice can solve whole circuit with either method Resistors in Series (EC3) • Resistors in series add to give the total resistance ∑ = = N j jtotal RR 1 • Example: total of 1, 2, and 3 Kohm resistors in series • Thus total is Ω=++=++= KRRRRtotal 6300020001000321 • Resistors in series law comes directly from KVL Resistors in Parallel • Resistors in parallel: • Inverse of the total equals the sum of the inverses ∑ = = N j jtotal RR 1 11 This comes directly from KCL at the node ∑∑ == === N j j N j j total total R VI R VI 11 • NOTE: inverse of resistance called conductance (G) • Unites are mhos (ohms spelled backwards) ∑ = = N j jtotal GG 1 • Thus when work in conductance change parallel to series
