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a/ Draw a series circuit with a 12 V source and R 1 = 100 W and R 2 = 200 W resistors.

Questions of the Day:. a/ Draw a series circuit with a 12 V source and R 1 = 100 W and R 2 = 200 W resistors. b/ Now add an ammeter and voltmeter to show how you would measure total I and V. c/ Redraw the circuit with ammeter and voltmeter

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a/ Draw a series circuit with a 12 V source and R 1 = 100 W and R 2 = 200 W resistors.

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  1. Questions of the Day: a/ Draw a series circuit with a 12 V source and R1 = 100 W and R2 = 200 W resistors. b/ Now add an ammeter and voltmeter to show how you would measure total I and V. c/ Redraw the circuit with ammeter and voltmeter to show how you would measure I1 and V1. d/ Redraw the circuitwith ammeter and voltmeter to show how you would measure I2 and V2.

  2. Parallel Circuits – more than one path (branch)

  3. have more than 1 path for current Parallel circuits - ________________________________________ _________________________________________ could have switches, etc. I wire wire wire high wire ________ potential + circuit element ___ circuit element ___ circuit element ___ circuit element ___ voltage source 1 2 3 - low ________ potential wire I Assume: 1. _____________________________________________________ 2. _____________________________________________________ 3. _____________________________________________________ 4. _____________________________________________________ All energy from source is used in each 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.

  4. For a circuit with 2 resistors: I2 I I I1 V V2 V1 R2 I2 R1 I1 I1 I2 I Energy _______________ Conservation: V = V1 = V2 Charge _______________ Conservation: I = I1 + I2 Equivalent _______________ (Total) R: 1/Req = 1/R1 + 1/R2 I Req Ohm’s __________ Law applies to the total: V = and to each individual element: V1 = V2 = I1R1 I2R2

  5. V = IR Ohm’s Law I = V/R

  6. Ex. Find all the voltages and currents in the circuit below: I 50W 100W 20. V V = V1 = V2 I1= V1/R1 50W 20. V V1 = I1 = R1 = 20/50 A 0.40 A I2= V2/R2 100W 20. V V2 = I2 = R2 = 0.20 A 20/100 A 33W 20/.60V/A 0.60 A 20. V V = I = Req = Req= V/I I = I1 + I2

  7. 1 Req 1 R2 1 R1 = + To find Req without using V and I: 1 Req 1 100 W 1 50 W = + 1 Req + 0.02 = 0.01 1 Req = 0.03 = Req 1/0.03 = 33 W parallel NOTE: In a ________________ circuit, Req is __________________ either R1 or R2. smaller than

  8. less More resistors in parallel  ________ total resistance  ________ total current more Circuit breaker or fuse opens the circuit if there is too much current.

  9. 100 W 100 W 80 W 200 V Ex. Speakers in parallel Req is smaller than the smallest Ex. Which bird is in danger?

  10. Compare the _________ of the resistances R1/R2 to the __________ of the currents: I1/I2. ratio ratio 50W 100W 20. V R1 50W = 1/2 100W R2 But… I1 0.4 A = 2/1 I2 0.2 A • I “divides up” ______________________________ to the R’s • R1 has ______ the current b/c it has __________resistance. • Parallel circuits are _______________________________. in inverse proportion (1/2)x 2x current dividers

  11. disconnected Notice what happens if one branch is __________________ : I1= V1/R1 = 20 V/50 W 50W 20. V 100W = 0.4 A no I I2= V2/R2 no I = 20 V/100 W 100W 20. V 50W = 0.2 A These are ____________________ answers as before. Each branch is_______________________of the others. This is why __________________ circuits are used. the same independent parallel

  12. + back to ____ side of the battery Plot V vs. “distance around circuit.” ____ side of battery + wire wire 20 100 W potential difference (V) ____ resistor 50 W _____ resistor - at the ___ side of the battery wire wire 0 distance around circuit R = 0 No ______ drop across wires because we assume _________

  13. 100 W 75 W 120 V Ex. A 3-way light has two filaments (wires) in parallel: Circuit symbols: One click  only the 100 W filaments connected. Two clicks  both the 100 W and the 75 W filaments are connected.

  14. Important: “V is ______________ everywhere in ___________ circuit” does NOT mean that V is ___________ in ______________ circuit! a parallel the same every other the same 10. V 10. V V= V1= V2= R1 = R2= 10. V 75W 25W 10. V 20. V V = V1 = V2 = R1 = R2= 20. V 20. V 75W 25W 20. V V is the _______________ across all parts of the second circuit, but it is a ________________ V than the first one! same different

  15. Equivalent resistance: _________________________________ ________________________________________________________ If you replace the resistors of a circuit with one resistor, the total I would be the same Replacing this part of the circuit with a single _______________ resistor: Req = 1/(1/R1 + 1/R2) = = = equivalent 20. V 50W 100W 1/(1/50 + 1/100) 1/(3/100) 33 W …gives you this circuit: V Req The total I = = 20. V 33 W 20. V Req = 33 W = 0.6 A same I This is the ____________ as before.

  16. parallel All _______________ circuits can be ___________________ in this way. simplified A. V = 3.0 V V = 3.0 V 40 Req = ____W 80W 80W voltage source This can be done even if the ______________________ is not shown. B. Req = _____W 8W 10.W 4.4 C. Req = _____W 15W 15W 15W 5 original same I Req results in the _____________ as the _________________ circuit.

  17. Alternative ways to draw parallel circuits: The circuit at left can also be drawn: R2 R1 V R1 R2 V R1 R1 or: or: R2 R2 V V NOTE: The diagram below is _________________________ because there is ________________ __________ for the current. not a parallel circuit only one R1 path V R2

  18. Ex 1. Draw two 10-W resistors in parallel between points A and B. Ex 2. Draw three 60-W resistors in parallel between points A and B. A 10 W 60 W 60 W 60 W 10 W A B B What is the equivalent resistance between points A and B in each of the examples above? (Hint: For identical parallel resistors, divide 1 R by the ___________ of resistors.) number 5 W 10 W 2 Ex 1: Divide _______ by ____  Req = __________ Ex 2: Divide _______ by ____  Req = __________ 3 60 W 20 W

  19. Parallel Circuit __________ Hookups: Original circuit: Meter V R1 R2 A. To measure, V1, the voltage across R1, connect the ______________ across R1. voltmeter disconnect To measure I1, the current through R1, _________________ the circuit and _____________ an ________________ next to R1 ammeter insert A R2 V V R1 ____ = where the ammeter could also be placed.

  20. across B. To measure the voltage _____________ and the current __________ resistor R2: through A V R1 ___ = optional ammeter position V R2 total C. To measure the _________ voltage and current : A R1 R2 V V ___ = optional ammeter position

  21. voltages In an ideal parallel circuit, all of the ______________ are equal, so placing the ________________ across any element gives ___________________________ . voltmeter the same result V V V R2 R1 V In reality, each voltage will _______________________ . This is because the wires have a small amount of ______ , and so by Ohm's law: __________ , there is a small amount of _________________ dropped along each wire. be slightly different R V = IR voltage

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