Practice Test DC circuits

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7 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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A
P Physics C


Name:

Electric Circuits Exam


Period:




1.













a.

List the light bulbs in order of brightness, from brightest to least bright. Justify your answer.




b.

Calculate the power dissipated by the 12
Ω
light bulb.





























c.

A capacitor is added to the circuit as shown abo
ve. The switch is closed at
t
= 0. On the axis
below sketch the magnitude of the potential difference
V
cap
across the capacitor as a function
of time, from when the switch is closed until a long time after the switch is closed. Mark any
important parts
to the graph.





















For
parts
d,e assume the 12
Ω
light bulb has burned out

42V

10
Ω

12
Ω

6.0
Ω

42V

10
Ω

12
Ω

6.0
Ω

5.0 µF

S

V
cap

t

A
P Physics C


Name:

Electric Circuits Exam


Period:

d.

Calculate at what time the capacitor has half of the total charge possible.









e.

Calculate the energy stored in the capacitor after a long time.






















2.

Consider th
e circuit shown. Initially the
capacitor is uncharged. At time
t
= 0, the
switch
S is c
losed and the capacitor begins
charging.




a.

Let’s say I am able to set V
0
, R, and C to whatever values I want (by simply choosing the



right po
wer supply, resistor, or capacitor).




i.

If I want to increase the amount of charge ultimately stored in the capacitor, which of



these should I change, and in what direction (higher or lower)? Explain.







ii.

If I want to decrease the amount of ti
me it takes for the capacitor to charge, which of




these should I change, and in what direction (higher or lower)? Explain.








iii.

If I want to increase the amount of energy ultimately stored in the capacitor, which of



these should I change, and
in what direction (higher or lower)? Explain.




V
o

C

R

A
P Physics C


Name:

Electric Circuits Exam


Period:




b.

Write down but do not solve the differential equation that tells me how the
charge
on the



capacitor varies with time.







c.

Show that the function Q(
t
) = CV
0
(1

e

t
/RC
) is a solution to your eq
uation in (b).









3.
The capacitance of a parallel
-
plate capacitor can be computed with the formula C = εA/d,
where A is the area of the plates, d is the separation distance, and ε is the permittivity of the
dielectric placed between the plates.



a.

Water has a relative p
ermittivity of ε/
ε
0
=
80
compared to the vacuum. Explain how a



water
-
filled capacitor will differ in its performance from an “air
-
gap” capacitor. Include



in your explanation a sketch that shows
how
and
why
the water will affect the capacitor.













b.

Suppose you need to make a 15 millifarad (mF) capacitor. What should its physical



dimensions be? Be sure to state which dielectric (air or water) you are using.














A
P Physics C


Name:

Electric Circuits Exam


Period:


c.

How long would it take to charge your capacitor with a 12 V battery passi
ng current



through a 250
Ω resistor?









d.

Let’s say you have several 15 mF capacitors but you really need a single 10 mF




capacitor. How might you wire these capacitors up to mimic a single 10 mF capacitor?












4.

You have a 120 V power supply and want to use it to dissipate
20 W of power in a resistor (or

set of resistors) so you can use the resistor to warm water. You have plenty of 1 Ω “power”

resistors (very fat resistors that can handle a lot of power). Design a circuit that will

accomplish this goal.