Series Circuits: Other examples:

Series circuits - ________________________________________ _________________________________________ have only 1 path for current could have switches, etc. I circuit element ___ 1 wire wire ________ potential high + voltage source circuit element ___ 2 low - ________ potential wire circuit element ___ wire 3 I Assume: 1. _____________________________________________________ 2. _____________________________________________________ 3. _____________________________________________________ 4. _____________________________________________________ All energy provided by source is used in the elements Wires have no potential drop (voltage) across them Pos. current is out of the “high” voltage side No charge is “lost.” All current returns to the source.

_______________ Conservation: V = V1 + V2 Charge For a circuit with 2 resistors: I V I1 V1 R1 I2 R2 V2 Energy _______________ Conservation: V = V1 + V2 Charge _______________ Conservation: I = I1 = I2 Equivalent _______________ (Total) Resistance: Req = R1 + R2 __________ Law applies to the total: V = and to each individual element: V1 = V2 = Ohm’s I Req I1R1 I2R2

V = IR Ohm’s Law I = V/R

Ex. Find all the voltages and currents in the circuit below: I = I1 = I2 V1 = I1R1 V1 = I1 = R1 = 5.0 V 0.125 A 40 W V2 = I2R2 V2 = I2 = R2 = 15.0 V 0.125 A 120 W 20. V 20/160 A V = I = Req = 0.125 A 160 W I = V/Req Req = R1 + R2

Form the _________ of each resistance to Req = _______ , and then multiply by the __________ voltage V ratio 160 W total V = 20. V R1 40 W 40 W x 20 V = 5 V Req 160 W 120 W R2 120 W x 20 V = 15 V Req 160 W V “divides up” ______________________________ as the R’s This is because ___________ R requires _________ energy. Series circuits are _______________________________. in the same proportion more more voltage dividers

Plot V vs. “distance around circuit.” back to ____ side of the battery + Plot V vs. “distance around circuit.” ____ side of battery + wire 20 V dropped across the ______ resistor 40 W 15 wire potential difference (V) V dropped across the ______ R - at the ___ side of the battery 120 W wire distance around circuit ______ drop across wires because we assume _________ No R = 0

“I is ______________ everywhere in ___________ circuit” does Important: “I is ______________ everywhere in ___________ circuit” does NOT mean that I is ___________ in _________________ circuit! the same a series the same every other I= I1= I2= 10/100 = .1 A 10. V R1= 25 W .1 A R2 = 75 W .1 A I= I1= I2= I3 = 10/200 = .05 A R1= 100 W 25 W 10. V R2= .05 A .05 A R3= 75 W .05 A same I is still the _______________ in all parts of the second circuit, but it is a ________________ I than the first one! different

If you replace the resistors of a circuit with one resistor, the total I would be the same Equivalent resistance: _________________________________ ________________________________________________________ Replacing this part of the circuit with a single _______________ resistor: Req = R1 + R2 = = 20. V 40 W equivalent 40 W + 120 W 120 W 160 W …gives you this circuit: V Req The total I = = 20 V 160 W 20. V Req = 160 W = 0.125 A This is the ____________ as before. same I

All _______________ circuits can be ___________________ in this way. series simplified A. Req = _____ W V = 20 V V = 20 V 50 W 200 150 W B. Req = _____ W 8 W V = 12 V 16 W 24 V = 12 V voltage source This can be done even if the ______________________ is not shown. C. Req = _____ W 70 W 90 20 W D. 10 W Req = _____ W 5 W 50 15 W 20 W Req results in the _____________ as the _________________ circuit. same I original

To measure I1, the current through R1, _________________ Meter __________ Hookups: Original circuit: R1 V R2 disconnect To measure I1, the current through R1, _________________ the circuit and _____________ an ________________ next to R1 insert ammeter insert disconnect A V R1 R1 V R2 R2 Other possibilities: R1 V V R1 R2 R2 A A ___ is the same everywhere, so _________________________ I anywhere gives same I.

To measure, V1, the voltage across R1, __________disconnect the circuit. Simply connect the ______________ across R1 do NOT voltmeter V R1 R2 V R1 R2 Original circuit: V Other possibilities: V R1 R2 V V V R1 R2 Similarly, to measure the _________ voltage V or V2: total V R1 R2 V R1 R2 V V