Assignment 15
Due: 11:00pm on Friday, December 4, 2009
Note:
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Electricity and Water Analogy
Learning Goal:
To understand the analogy between water pressure, water flow, voltage, and current
As suggested by the fact that we call both
currents,
the flow of charged particles through an electrical circuit is analogous in
some ways to the flow of water through a pipe.
When water flows from a small pipe to a large pipe, the flow (measured, for instance, in gallons per minute) is the same in
both pipes, because the amount of water entering one pipe must equal the amount leaving the other. If not, water would
accumulate in the pipes. For the same reason, the total electric current
is constant for circuit elements in series.
Water pressure is analogous to total electric potential (voltage), and a pump is analogous to a battery. Water flowing
through pipes loses pressure, just as current flowing through a resistor falls to lower voltage. A pump uses mechanical work
to raise the water's pressure and thus its potential energy; in a battery, chemical reactions cause charges to flow against the
average local electric field, from low to high voltage, increasing their potential energy.
Part A
Consider the following water circuit: water is continually
pumped to high pressure by a pump, and then funnelled into
a pipe that has lower pressure at its far end (else the water
would not flow through the pipe) and back to the pump. Two
such circuits are identical, except for one difference: the
pipes in one circuit have a larger diameter than the pipes in
the other circuit. Through which circuit is the flow of water
greater?
ANSWER:
Small pipe
Large pipe
Correct
The cross sectional area of the pipe is analogous to the area of a wire: the smaller the area the higher the resistance
and the more the pipe/wire impedes flow. If the change in pressure (proportional to the potential energy per unit
mass) of water traveling through two pipes is the same, the flow will be less through the pipe with smaller cross
sectional area. The electrical analog is Ohm's law
, where resistance
is inversely proportional to the area
of a wire/resistor.
Part B
Now consider a variant on the circuit. The water is pumped to high pressure, but the water then faces a fork in the pipe.
Two pipes lead back to the pump: large pipe L and small pipe S. Since the water can flow through either pipe, the pipes
are said to be
in parallel
:
The overall flow of water that enters the system before the
fork is equal to _____
Hint B.1
Water conservation
Hint not displayed
ANSWER:
the flow through pipe L.
the sum of the flows through L and S.