6 DC Circuit III

6 DC Circuit III - ELEC101 DCcircuits66 2010/11Spring...

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ELEC 101 DC circuits 66 2010/11 Spring Equivalence Two resistive one-port networks are equivalent if they have the same current- voltage (I-V) curve across the two terminals for ALL loads (or sources). V1 Network A load R I1 V2 Network B load R I2 Hence a complex network (Network A) can be replaced by a simple equivalent (Network B) and network analysis can be simplified. If I1 = I2 and V1 = V2 for ALL load R , then network A and network B are equivalent . ( A B ) Example NO. I1 I2 and V1 V2 for other R. For example, when R = 6 , I1 = 0.5A, V1 = 3V ; I2 = 2/3A, V2 = 4V Is network A equivalent to network B ?? 2 6 8V R = 2 4V R = 2 I1 = 1A I2 = 1A V1 = 2V V2 =2V network A network B Example
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ELEC 101 DC circuits 67 2010/11 Spring Network A equivalent to network B ? ( YES. For ALL R , I1 = I2, V1= V2 ) network A network B 2 4V 4 8V 4 R R I2 V2 V1 I1 Example network A network B 2 4V 4 8V 4 R R I2 V2 V1 I1 When R = 0 (short) A V I V V 2 2 4 1 0 1 A V I V V 2 4 8 2 0 2 network A network B 2 4V 4 8V 4 R R I2 V2 V1 I1 When R =  (open) V V A I 4 1 0 1 20 8 24 4 8 IA V VV  a b I1 I2 V1 For example, when R = 2 , I1 = 1A, V1 = 2V ; I2 = ?, not easy to calculate.
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ELEC 101 DC circuits 68 2010/11 Spring For network A The I1-V1 curve for all R is the line joining R = 0 and R = . The curve is a straight line as the I-V curve for a resistive circuit is linear. For network B c d Hence I1-V1 curve = I2-V2 curve. Hence network A and network B are equivalent . e Similarly the I2-V2 curve is a straight line. I2 V2 2A 4V R = 0 R = 0 I1 V1 2A 4V R = 0 R = 0 In general, such a straight line is called the load line of the circuit
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ELEC 101 DC circuits 69 2010/11 Spring Load line •A load line is a straight line in a current voltage plot •U s e f u l for analyzing nonlinear circuit elements and loads l s o useful for power analysis Assume the load to be 0 and ohms (short circuit and open circuit situations) Kirchhoff’s voltage law : Complex circuit with power supply Load R V o I V V IR o I V Close circuit current = V o /R Open circuit voltage = V o Load line
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ELEC 101 DC circuits 70 2010/11 Spring 7 Example 7 18V V 1 I 1 Show that network A and network B are equivalent. 36V 3 6A 4 R I 2 V 2 1. when R = 0 (short) , 1 1 0 18 18 77 VV V IA  2 22 2 0 36 3 (6 ) 4 18 18 VA II V   2. when R =  (open) , 1 1 0 18 3. I 1 -V 1 curve = I 2 -V 2 curve Network A Network B Hence network A and network B are equivalent . R 18V 36V 3 6A 4 V 18 3 A 6 V 36 V source A 6 across voltage V A 0 I 2 2 2 3k 1k 12V O I 6k 3k 3V 2k Find I O . a V 12V 6k 3k 3V 2k 3k 1k Hence the circuit can be converted to : Hence V a can be found using node voltage (KCL) method .
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This note was uploaded on 03/27/2011 for the course ELEC 212 taught by Professor Prof.matthewmckay during the Spring '11 term at HKUST.

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6 DC Circuit III - ELEC101 DCcircuits66 2010/11Spring...

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