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# L3 electrical circuits

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### L3 electrical circuits

1. 1. Analysis of Electric Circuits
2. 2. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 2 Electric Circuit Electric Circuit An interconnection of simple electrical devices with at least one closed path in which current may flow Circuit Elements Active Elements Voltage and Current sources Passive Elements Resistors, Inductors and Capacitors
3. 3. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 3 Circuit Elements Review topics Basic Circuit ElementsBasic Circuit Elements Active ElementsActive Elements Passive ElementsPassive Elements SourcesSources Dependent sources Dependent sources Independent sources Independent sources Voltage sourcesVoltage sources Current sourcesCurrent sources Ideal (DC) Voltage source Ideal (DC) Voltage source Ideal (DC) Current source Ideal (DC) Current source Practical (DC) Current source Practical (DC) Current source Practical (DC) Voltage source Practical (DC) Voltage source 1. Resistors 2. Inductors 3. Capacitors 1. Resistors 2. Inductors 3. Capacitors
4. 4. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 4 Passive Elements Resistance (R): Property of opposition to flow of current The voltage across the resistor is proportional to the current flowing through it VR = IR ‘R’ = VR/I Unit - Ohm
5. 5. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 5 Passive Elements Inductance (L): Property of opposition to the rate of change of current The voltage induced in the inductor is proportional to the rate of change of current flowing through it eL = L (di/dt) = N (dФ/dt) L = N (dФ/di) Unit – Henry (H)
6. 6. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 6 Passive Elements Capacitance (C): Property which opposes the rate of change of voltage The capacitive current is proportional to the rate of change of voltage across it ic = C (dv/dt) Unit – Farad (F).
7. 7. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 7 Ideal Nature Property of the element which does the intended work only ideal voltage source maintains a prescribed voltage regardless of the current in the device. Internal resistance Rs = 0 ideal current source maintains a prescribed current regardless of the voltage across the device. Internal resistance Rs = ∞ ideal resistor constraints its voltage and current to be proportional to each other. (v = iR; Ohm’s law)
8. 8. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 8 Ideal Sources Independent Voltage & Current Source: I d e a l C u r r e n t S o u r c e ( D C ) + - I d e a l V o l t a g e S o u r c e ( D C ) V s V s I s
9. 9. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 9 Practical Sources Independent Voltage & Current Sources P r a c t i c a l C u r r e n t S o u r c e + - P r a c t i c a l V o l t a g e S o u r c e V s I s R s R s
10. 10. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 10 Source Transformation Conversion of Practical Voltage source to Current source & vice versa Vs Rs + - + - a b Ip Rp + - a b Voltage & Current sources shown in the figure are electrically equivalent if Vs = Ip * Rp or (Ip = Vs/Rs) Rs = Rp
11. 11. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 11 Dependent Sources: Voltage Controlled Voltage Source (VCVS) + V = u V a b c d a b + - - V Voltage Controlled Current Source (VCCS) + I = u V a b c d a b + - - I Voltage Controlled:
12. 12. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 12 Dependent Sources: Current Controlled Voltage Source (CCVS) + V = u I a c d a b + - - I a V Current Controlled Current Source (CCCS) + I = u I a c d a b + - - I a I Current Controlled: