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

2. 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.

3. _______________ 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: /Req =
1/R1 + 1/R2
__________ Law applies to the total: V =
and to each individual element: V1 =
V2 =
Ohm’s
I Req
I1R1
I2R2

5. V = IR
Ohm’s
Law
I = V/R

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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/ /100)
1/(3/100)
33 W
…gives you this circuit: V
Req
The total I =
= V
33 W
20. V
Req =
33 W
= 0.6 A
This is the ____________ as before.
same I

13. 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

14. 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

15. 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

16. 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.

17. 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

18. 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