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Electric Circuits Name:
Parallel Circuits
Read from Lesson 4 of the Current Electricity chapter at The Physics Classroom :
http://www.physicsclassroom.com/Class/circuits/u9l4a.html
http://www.physicsclassroom.com/Class/circuits/u9l4c.html
MOP Connection: Electric Circuits: sublevels 8, 10 and 11
Review:
- A circuit in which all charge follows a single pathway is a ____ circuit; a circuit in which charge
follows multiple pathways is a ____ circuit.
a. series, parallel b. parallel, series
- For a parallel circuit: as the number of resistors being used within the same parallel circuit increases,
the overall resistance value _____________________________ (increases, decreases) and the overall
current value _____________________________ (increases, decreases).
- Household circuits are connected in parallel so that _____. Select all that apply.
a. houses get the same effect with less current and thus save on energy costs
b. the turning off of one appliance does not result in the shut down of others
c. the hazard of electrocution and overheating of circuits is avoided
Water Analogy:
- When the water flow (or charge flow) is divided into two or more separate pathways (as in a parallel
circuit) the sum of the current in each individual pathway equals the total current. Utilize this
principle to fill in the blanks in the following two diagrams. The meters in the diagram are
measuring water flow rates in gallons per minute ("gpm").
- Apply the same principle to fill in the blanks in the following diagrams for charge flow (i.e., current)
through a parallel circuit.
Electric Circuits
The Staircase Analogy
Electric charge dividing into multiple pathways in a parallel circuit is analogous to people walking
down stairs which divide up into separate paths.
Imagine being at a large shopping mall; you are descending a rather wide stairway when all of a
sudden it breaks up into several smaller stairways. Being in a hurry, you scan the different
pathways down the stairs to see which path is least crowded. You finally decide that the left
stairway is least crowded and make a "dash" towards it. You know that your "flow rate" will be
greatest along the stairway with the least resistance. When the "people flow" divides up into
multiple pathways, each pathway has the same change in height (or same gravitational potential
drop); yet, the pathway that offers the least resistance will have the greatest flow rate.
In an analogous manner, as charge flow divides up into multiple pathways in a parallel circuit, each
pathway has the same electric potential drop; yet, the pathway with the least resistance will have
the greatest rate of charge flow (i.e., current).
- In the following circuits, fill in the blanks to indicate the current through the different pathways.
Calculate the resistance of each resistor. Then rank the resistance of the resistors (labeled A , B , and
C ) in order from smallest to largest.
Ranking of Resistance Ranking of Resistance
____ < ____ < ____ ____ < ____ < ____
- A three-resistor parallel circuit is created. The resistances of the resistors are 3 Ω, 6 Ω, and 9 Ω.
Suppose that one observes the current through the 3 Ω resistor to be 6 Amperes. The voltage drop
across this 3 Ω resistor must be _______ V. This provides sufficient evidence to conclude that the
voltage drop across the 6 Ω resistor is _______ V and the voltage drop across the 9 Ω resistor is
_________ V. Therefore, the current in the 6 Ω resistor is ________ Amperes and the current in the 9
Ω resistor is _________ Amperes. When these three branch currents combine, one would observe
that the current in the ___________ V battery is _________ Amperes. In summary:
R
1
= 3 Ω R
2
= 6 Ω R
3
I
1
= 6 Amps I
2
= _____ Amps I
1
= _____ Amps
ΔV
1
= _____ V ΔV
2
= _____ V ΔV
3
= _____ V
I
battery
= _____ Amps ΔV
battery
= _____ V ΔV
battery
/ I
battery
= ________
- Consider the circuit at the right.
a. There is a voltage drop of _____V across each 2-Ω resistor.
b. By Ohm's law, the current in each 2-Ω resistor is _____ amps.
c. The current through the battery is ______ amps.
d. The resistors in parallel offer a combined resistance of _______ Ω
to the charge being pumped by the battery.
Electric Circuits
- For each of the following branched systems, determine the equivalent resistance.
a.
is equivalent to
_______ Ω
b.
is equivalent to
_______ Ω
c.
is equivalent to
_______ Ω
d.
is equivalent to
_______ Ω
e.
is equivalent to
_______ Ω
f.
is equivalent to
_______ Ω
g.
is equivalent to
_______ Ω
h.
is equivalent to
_______ Ω
i.
is equivalent to
_______ Ω
j.
is equivalent to
_______ Ω
k.
is equivalent to
_______ Ω
l.
is equivalent to
_______ Ω
- Four resistors are connected in a parallel circuit. Three of the resistance values are known - 3 Ω, 4 Ω
and 6 Ω. The overall or equivalent resistance of the four resistors must be ____ Ω. (Choose the one
answer that is most informative.)
a. greater than 3 b. greater than 6 c. greater than 13
d. less than 13 e. less than 3 f. ... it is impossible to tell.
