ResistiveCircuitspp2

ResistiveCircuitspp2 - RESISTIVE CIRCUITS Here we introduce...

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1 RESISTIVE CIRCUITS Here we introduce the basic concepts and laws that are fundamental to circuit analysis LEARNING GOALS • OHM’S LAW - DEFINES THE SIMPLEST PASSIVE ELEMENT: THE RESISTOR • KIRCHHOFF’S LAWS - THE FUNDAMENTAL CIRCUIT CONSERVATION LAWS- KIRCHHOFF CURRENT (KCL) AND KIRCHHOFF VOLTAGE (KVL) • LEARN TO ANALYZE THE SIMPLEST CIRCUITS • SINGLE LOOP - THE VOLTAGE DIVIDER • SINGLE NODE-PAIR - THE CURRENT DIVIDER • SERIES/PARALLEL RESISTOR COMBINATIONS - A TECHNIQUE TO REDUCE THE COMPLEXITY OF SOME CIRCUITS • CIRCUITS WITH DEPENDENT SOURCES - (NOTHING VERY SPECIAL) • WYE - DELTA TRANSFORMATION - A TECHNIQUE TO REDUCE COMMON RESISTOR CONNECTIONS THAT ARE NEITHER SERIES NOR PARALLEL RESISTORS + ) ( t v ) ( t i A resistor is a passive element characterized by an algebraic relation between the voltage across its terminals and the current through it Resistor a for Model General )) ( ( ) ( t i F t v = A linear resistor obeys OHM’s Law ) ( ) ( t Ri t v = The constant, R, is called the resistance of the component and is measured in units of Ohm ) ( From a dimensional point of view Ohms is a derived unit of Volt/Amp ) 10 ( ) 10 ( 3 6 Ohm Kilo Ohm Mega Ohm of Multiples Standard k M k in resistance in resulting mA Volt is occurrence common A Conductance If instead of expressing voltage as a function of current one expresses current in terms of voltage, OHM’s law can be written v R i 1 = Since the equation is algebraic the time dependence can be omitted Gv i R G = = write and component the of e Conductanc as define We 1 The unit of conductance is Siemens
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2 Some practical resistors Symbol R + v i ation Represent Circuit Notice passive sign convention Two special resistor values Circuit Short Circuit Open = + 0 v 0 = i = = G R 0 0 = = G R Linear approximation Linear range Ohm’s Law is an approximation valid while voltages and currents remain in the Linear Range iR Ri v = = v i Actual v-I relationship “A touch of reality” Gv i = R R + v i + v i iR v = iR v =
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3 OHM’S LAW PROBLEM SOLVING TIP Law s OHM' Gv i Ri v = = One equation and three variables. Given ANY two the third can be found Given current and resistance Find the voltage A I 2 = = 5 R = + ] [ 10 V V Notice use of passive sign convention Given Current and Voltage Find Resistance + ] [ 20 V ] [ 4 A I = I V R = = 5 R Given Voltage and Resistance Compute Current + ] [ 12 V = 3 R R V I = ] [ 4 A I = Determine direction of the current using passive sign convention Table 1 Keeping Units Straight Voltage Current Resistance Volts Amps Ohms Volts mA k mV A m mV mA RI V =
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4 UNITS? CONDUCTANCE IN SIEMENS, VOLTAGE IN VOLTS. HENCE CURRENT IN AMPERES ] [ 8 ) ( A t i = GIVEN VOLTAGE AND CONDUCTANCE REFERENCE DIRECTIONS SATISFY PASSIVE SIGN CONVENTION ) ( ) ( t Gv t i = OHM’S LAW + OHM’S LAW ) ( ) ( t Ri t v = ] [ 2 ) ( ) ( ) 2 ( ] [ 4 A t i t i V = = UNITS?
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ResistiveCircuitspp2 - RESISTIVE CIRCUITS Here we introduce...

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