Parallel Circuits – more than one path (branch)

Parallel circuits - ________________________________________ _________________________________________ have more than 1 path for current could have switches, etc. I wire high wire wire ________ potential wire + 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.

_______________ Conservation: V = V1 = V2 Charge For a circuit with 2 resistors: I2 I I I1 V V2 I1 R1 V1 I2 R2 I1 I2 I Energy _______________ Conservation: V = V1 = V2 Charge _______________ Conservation: I = I1 + I2 Equivalent _______________ (Total) R: 1/Req = 1/R1 + 1/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: V = V1 = V2 I1= V1/R1 V1 = I1 = R1 = 20. V 0.40 A 20/50 A 50 W I2= V2/R2 V2 = I2 = R2 = 20. V 20/100 A 0.20 A 100 W 33 W V = I = Req = 20. V 0.60 A 20/.60 V/A Req= V/I I = I1 + I2

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

Compare the _________ of the resistances R1/R2 to the __________ of the currents: I1/I2. ratio ratio 50 W 20. V 100 W R1 50 W = 1/2 R2 100 W 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 2x (1/2)x current dividers

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

Plot V vs. “distance around circuit.” 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 distance around circuit ______ drop across wires because we assume _________ No R = 0

Important: “V is ______________ everywhere in ___________ circuit” does NOT mean that V is ___________ in ______________ circuit! the same a parallel the same every other 10. V V= V1= V2= 10. V R1 = R2= 10. V 75 W 25 W 10. V 20. V V = V1 = V2 = R1 = R2= 20. V 20. V 75 W 25 W 20. V V is the _______________ across all parts of the second circuit, but it is a ________________ V than the first one! same 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 = 1/(1/R1 + 1/R2) = equivalent 20. V 50 W 100 W 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 This is the ____________ as before. same I

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

Alternative ways to draw parallel circuits: The circuit at left can also be drawn: V R1 R2 V R1 R2 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

What is the equivalent resistance between points A 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 Ex 1: Divide _______ by ____  Req = __________ Ex 2: Divide _______ by ____  Req = __________ 10 W 2 60 W 3 20 W

A. To measure, V1, the voltage across R1, connect the 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.

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

In an ideal parallel circuit, all of the ______________ 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 V R1 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