Electric Circuits Answers

Inspector Clouseau has found a clue in his pursuit of The Phantom:5 a sheet of some
unknown material. He has a parallel plate capacitor and can measure the maximum
charge held by the plates. With air between them, this maximum charge is 23.9 pC.
He then slips the unknown material between them and finds a maximum charge of
134 pC. Using this information, find the dielectric constant of the unknown material
and determine its identity using the Table 16.1 in your text.

We spent all the physics budget on the computers in S168, meaning I needed a 4.0 µF
capacitor but didn’t have one. Fortunately, I was able to fake it by hooking up three
identical capacitors with two in parallel and one in series to make an equivalent capacitance
of 4.0 µF (see diagram). What is the capacitance of the individual capacitors
(to be clear again, the three capacitors each have the same rated capacitance)? If
I connect them to a 6.0 V battery, find the charge and potential difference on each
capacitor in the system.

Two capacitors have an equivalent capacitance of 16.0 pF when they are hooked up
in parallel. The same two capacitors when hooked up in series have an equivalent
capacitance of 1.75 pF. What is the capacitance of each capacitor?

It was a dark and stormy night.4 A cloud having a potential difference of 8.50 × 108 V
relative to a nearby tree discharges to the tree, delivering 1.75 × 109 J of energy.
Determine the capacitance of the cloud-tree system, as well as the amount of charge if
the discharge is complete (i.e., the final potential difference between the cloud and the
tree is zero). How many electrons does this amount of charge imply?

It’s Friday night, and you’ve got big party plans. What will you do? Why, make a
capacitor, of course! You use aluminum foil as the plates, and since a standard roll of
aluminum foil is 30.5 cm wide you make the plates of your capacitor square, each a
30.5 cm by 30.5 cm. You separate the plates with regular paper, which has a thickness
of 0.100 mm and a dielectric constant of kappa = 3.7. What is the capacitance of your
capacitor? If you connect it to a 9 V battery, how much charge is stored on either
plate?

An alpha particle (mass of 6.64 × 10−27 kg, charge of +2e - or twice the fundamental
unit of charge) is shot with an initial velocity of 2.00×107 m/s directly at a gold nucleus
(charge of +79e, and assumed to remain stationary so you will not need its mass). If
you assume that the alpha particle was initially very far from the gold nucleus, there
is no potential energy associated with the alpha particle - gold nucleus system. If the
alpha particle is fired directly at the gold nucleus, it will get close to the gold nucleus
before being repelled. How close to the gold nucleus will the alpha particle get (note
that at its closest, the alpha particle will have v = 0 m/s)?3

An electron is fired horizontally with an initial velocity of 4.20 × 106 m/s between a
pair of horizontal plates. The plates are separated by a distance of 1.20 mm and are
charged to have a potential difference of 120 V, with the bottom plate being at the
higher potential. If the electron is midway between the plates when it is fired, how far
from its entry point will it strike the bottom plate? You may ignore the acceleration
due to gravity in this problem so that the force on the electron is entirely due to
electrostatics (but think about why this assumption is OK!).

Ororo Munroe uses her ability to manipulate lightning to electrocute Mortimer Toynbee.1
She is also sensitive to electric potential and can measure the potential at her
location. When she zaps Mortimer, she finds that the potential is 6.50 × 105 V at
her position a distance of 4.75 m away from him. Given this information, what is the
charge on Mortimer? Treat him like a point Toad.

what is meant by range of an ammeter? also of voltmeter and galvanometer?