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Page 2 Superposition It states that, in any linear circuit containing multiple independent sources, the total current through or voltage across an element can be determined by algebraically adding the voltage or current due to each independent source acting alone with all other independent source set to zero. Source Transformation It states that as independent voltage source S V in series with a resistance R is equivalent to independent current source ? Ss I V / R in parallel with a resistance R. Or An independent current source S I in parallel with a resistance R is equivalent to a dependent source SS V I R ? in series with a resistance R. Thevenin’s Theorem It states that any network composed of ideal voltage and current source, and of linear resistor, may be represented by an equivalent circuit consisting of an ideal voltage source TH V in series with an equivalent resistance TH R . Methods to calculate thevein equivalent The therein voltage ? ? TH V is equal to open circuit voltage across load terminals. Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when all independent source are set to zero (voltage sources replaced by short circuit & current source by OC) Case – 1 : Circuit with independent sources only Page 3 Superposition It states that, in any linear circuit containing multiple independent sources, the total current through or voltage across an element can be determined by algebraically adding the voltage or current due to each independent source acting alone with all other independent source set to zero. Source Transformation It states that as independent voltage source S V in series with a resistance R is equivalent to independent current source ? Ss I V / R in parallel with a resistance R. Or An independent current source S I in parallel with a resistance R is equivalent to a dependent source SS V I R ? in series with a resistance R. Thevenin’s Theorem It states that any network composed of ideal voltage and current source, and of linear resistor, may be represented by an equivalent circuit consisting of an ideal voltage source TH V in series with an equivalent resistance TH R . Methods to calculate thevein equivalent The therein voltage ? ? TH V is equal to open circuit voltage across load terminals. Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when all independent source are set to zero (voltage sources replaced by short circuit & current source by OC) Case – 1 : Circuit with independent sources only To calculate TH V , open circuit of RL Using sources transformation ? ? ? ? TH 2 V 24 12V 22 To calculate Rth Short I & V sources & open 6mA source ? ? ? ? ? ? ? th R 1 2 1 1 2k Page 4 Superposition It states that, in any linear circuit containing multiple independent sources, the total current through or voltage across an element can be determined by algebraically adding the voltage or current due to each independent source acting alone with all other independent source set to zero. Source Transformation It states that as independent voltage source S V in series with a resistance R is equivalent to independent current source ? Ss I V / R in parallel with a resistance R. Or An independent current source S I in parallel with a resistance R is equivalent to a dependent source SS V I R ? in series with a resistance R. Thevenin’s Theorem It states that any network composed of ideal voltage and current source, and of linear resistor, may be represented by an equivalent circuit consisting of an ideal voltage source TH V in series with an equivalent resistance TH R . Methods to calculate thevein equivalent The therein voltage ? ? TH V is equal to open circuit voltage across load terminals. Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when all independent source are set to zero (voltage sources replaced by short circuit & current source by OC) Case – 1 : Circuit with independent sources only To calculate TH V , open circuit of RL Using sources transformation ? ? ? ? TH 2 V 24 12V 22 To calculate Rth Short I & V sources & open 6mA source ? ? ? ? ? ? ? th R 1 2 1 1 2k Case – 1 : Circuit with both dependent & independent sources Methodology 1: ? Th V can be found in same way. ? For TH R set all independent sources to zero. ? Remove load & put a test source test V across its terminals, let current through test source is test I . ? ? test TH test Thevenin resistance , V R I ? This method is must if independent sources are absent. Methodology 2: ? TH V is calculated in same way. ? For TH R short circuit load terminals & leave independent sources as it is ? Obtain SC I through load terminals. ? TH OC SC R V I ? Norton’s Theorem Any network composed ideal voltage & current sources, and of linear resistors, may be represented by an equivalent circuit consisting of an ideal current source N I in parallel with an equivalent resistance N R . ? ? N TH RR ? To calculate N I we short circuit load terminals & calculate short circuit current. ? Therein equivalent & Norton equivalent are dual of each other. Page 5 Superposition It states that, in any linear circuit containing multiple independent sources, the total current through or voltage across an element can be determined by algebraically adding the voltage or current due to each independent source acting alone with all other independent source set to zero. Source Transformation It states that as independent voltage source S V in series with a resistance R is equivalent to independent current source ? Ss I V / R in parallel with a resistance R. Or An independent current source S I in parallel with a resistance R is equivalent to a dependent source SS V I R ? in series with a resistance R. Thevenin’s Theorem It states that any network composed of ideal voltage and current source, and of linear resistor, may be represented by an equivalent circuit consisting of an ideal voltage source TH V in series with an equivalent resistance TH R . Methods to calculate thevein equivalent The therein voltage ? ? TH V is equal to open circuit voltage across load terminals. Therein resistance is input or equivalent resistance at open circuit terminals (load terminals) when all independent source are set to zero (voltage sources replaced by short circuit & current source by OC) Case – 1 : Circuit with independent sources only To calculate TH V , open circuit of RL Using sources transformation ? ? ? ? TH 2 V 24 12V 22 To calculate Rth Short I & V sources & open 6mA source ? ? ? ? ? ? ? th R 1 2 1 1 2k Case – 1 : Circuit with both dependent & independent sources Methodology 1: ? Th V can be found in same way. ? For TH R set all independent sources to zero. ? Remove load & put a test source test V across its terminals, let current through test source is test I . ? ? test TH test Thevenin resistance , V R I ? This method is must if independent sources are absent. Methodology 2: ? TH V is calculated in same way. ? For TH R short circuit load terminals & leave independent sources as it is ? Obtain SC I through load terminals. ? TH OC SC R V I ? Norton’s Theorem Any network composed ideal voltage & current sources, and of linear resistors, may be represented by an equivalent circuit consisting of an ideal current source N I in parallel with an equivalent resistance N R . ? ? N TH RR ? To calculate N I we short circuit load terminals & calculate short circuit current. ? Therein equivalent & Norton equivalent are dual of each other. Maximum Power Transfer Theorem: A load resistance L R will receive maximum power from a circuit when load resistance is equal to Thevenin’s/ Norton’s resistance seen at load terminals. ? L Th RR In case of AC circuit, this condition translates to ? L * th ZZ ? But if load is resistive in AC circuit then ? L Th RZ ? For maximum power transfer ? ? ? ? ? 2 2 LL Th Th R R X X ? For maximum power transfer L Th X X 0 ??Read More
1. What are circuit theorems? |
2. What is the importance of circuit theorems in electrical engineering? |
3. What are some commonly used circuit theorems? |
4. How does Thevenin's Theorem simplify circuit analysis? |
5. How is the Maximum Power Transfer Theorem useful in practical applications? |
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