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Series Circuits: Other examples: have only 1 path for current Series circuits - ________________________________________ could have switches, etc. _________________________________________ I high ________ potential wire circuit 1 element ___ + voltage source low ________ potential Assume: wire circuit 2 element ___ wire I circuit 3 element ___ wire All energy provided by source is used in the elements 1. _____________________________________________________ Wires have no potential drop (voltage) across them 2. _____________________________________________________ Pos. current is out of the “high” voltage side 3. _____________________________________________________ 4. _____________________________________________________ No charge is “lost.” All current returns to the source. For a circuit with 2 resistors: I V I1 R1 V1 I2 R2 V2 Energy _______________ Conservation: Charge _______________ Conservation: V = V1 + V2 Equivalent _______________ (Total) Resistance: Req = R1 + R2 I = I1 = I2 Ohm’s Law applies to the total: __________ and to each individual element: V = I Req V1 = I1R1 V2 = I2R2 V = IR Ohm’s Law I = V/R Ex. Find all the voltages and currents in the circuit below: 40 W 20. V 120 W V1 = I1R1 V1 = 5.0 V I = I1 = I2 I1 = 0.125 A V2 = I2R2 V2 = 15.0 V I2 = 0.125 A R2 = 120 W 20. V 0.125 A I = 20/160 Req = 160 W V = I = V/Req R1 = 40 W Req = R1 + R2 ratio of each resistance to Req = 160 Form the _________ _______ W , total and then multiply by the __________ voltage V V= 20. V 40 W 120 W R2 120 W Req 160 W R1 Req 40 W x 20 V = 5V 160 W x 20 V = 15 V in the same proportion •V “divides up” ______________________________ as the R’s more more •This is because ___________ R requires _________ energy. voltage dividers •Series circuits are _______________________________. + back to ____ side of the battery Plot V vs. “distance around circuit.” ____ + side of battery 20 15 potential difference (V) wire V dropped across 40 W resistor the ______ wire V dropped across the ______ 120 W R 0 wire at the ___ side of the battery distance around circuit R=0 No drop across wires because we assume _________ ______ Important: a series “I is ______________ everywhere in ___________ circuit” does the same every other the same in _________________ NOT mean that I is ___________ circuit! 10. V R1= 25 W I= 10/100 = .1 A I1= .1 A I2= .1 A R2= 25 W I= 10/200 = .05 A I1= .05 A I2= .05 A I3 = .05 A R2 = 75 W R1= 100 W 10. V R3= 75 W same I is still the _______________ in all parts of the second different circuit, but it is a ________________ I than the first one! Equivalent resistance: _________________________________ If you replace the resistors of a circuit with one resistor, the total I would be the same ________________________________________________________ 20. V 40 W 120 W Replacing this part of the circuit with a single equivalent _______________ resistor: Req = R1 + R2 = 40 W + 120 W = 160 W …gives you this circuit: The total I = 20. V Req = 160 W V = Req 20 V 160 W = 0.125 A same I This is the ____________ as before. series All _______________ circuits can be ___________________ in this way. simplified A. V= 20 V B. 150 W 8W 50 W 16 W V= 12 V V= 20 V Req = 200 _____ W V= 12 V Req = 24 _____ W voltage source This can be done even if the ______________________ is not shown. C. Req = 90 _____ W 70 W 20 W 10 W D. 5W 15 W 20 W Req = 50 _____ W original same I Req results in the _____________ as the _________________ circuit. Meter __________ Hookups: Original circuit: V R1 R2 disconnect To measure I1, the current through R1, _________________ ammeter the circuit and _____________ an ________________ next to R1 insert insert disconnect R1 V V R2 Other possibilities: V R2 A R1 A R2 R1 R1 V R2 A anywhere gives same I. ___ I is the same everywhere, so _________________________ do NOT To measure, V1, the voltage across R1, __________disconnect voltmeter the circuit. Simply connect the ______________ across R1 Original circuit: R1 V Other possibilities: R1 V R2 R2 V R1 V V V R2 R2 R1 V total Similarly, to measure the _________ voltage V or V2: V V R1 R2 R1 V R2 V