Download First Exam Sum15 Phys 1220

First Exam Sum15
Phys 1220
__________
name
Each problem is of equal value.
You can skip three problems according to the following rules:
You must work at least one of problems 3 and 4 and one of problems 5 and 8.
If you work more than 5 problems, we will grade all and count the best results
consistent with the above rules. Make sure you work first all required problems
before you start to work extra problems!
Tips for better exam grades:
Read all problems right away and ask questions as early as possible.
Make sure that you give at least a basic relevant equation or figure for each
sub-problem.
Make use of the entire exam time.
Show your work for full credit. The answer ‘42’ only earns you any credit IF
‘42’ is the right answer. We reserve points for ‘steps in between’, figures,
units, etc. If all you give us is a numeric answer you may receive only a C
grade for the problem and in some cases even less.
No credit given for illegible handwriting or flawed logic in an argument.
1. Electrostatics: Resistor Networks
Consider the circuit shown below.
a)
b)
c)
d)
Derive the series and parallel network rules for equivalent resistance.
Calculate the equivalent resistance of the circuit shown above.
Find the current through the 2 resistor.
What is the voltage drop across the 6 resistor closest to the
source?
2. Capacitors
Consider a capacitor network.
a) Derive the series and parallel rule for capacitor networks.
b) Three capacitors have capacitances of 8.4, 8.4, and 4.2 [F]. They are
connected in series across a 36[V] source. How much energy is stored in the
4.2[F] capacitor?
c) The capacitors are now disconnected from the source without allowing them to
discharge. They are then reconnected in parallel with each other. What is the
voltage across each capacitor now?
3. Electrostatics, lab
Measurement instruments
a) Explain how to use an ammeter and a voltmeter to measure electrical
properties in a circuit:
b) If you need to measure the current and voltage drop across a resistor
simultaneously, what complications arise?
c) Consider a resistor network of three resistors. Two are in parallel with each
other and one is in series with the parallel arrangement. Neglect wire
resistance. How many currents and voltages can you measure in this circuit
when it is connected to a battery in series with the series arrangement of the
resistors? Hint: Draw the network and indicate the placements of the ammeter
and voltmeter for the various readings.
4. Electrostatics: Lecture video discussion
Recall the lecture videos on demonstrating Coulomb’s Law.
a) Describe the experimental setup.
b) Explain what causes the observed deviation from the 1/r2 law at short
distances and discuss a theoretical correction of it.
c) The data for a certain distance are r= 1[m], FC = 1.2, 1.8, 1.8 [N] for
successive readings of the force, calculate the mean and the standard
deviation.
5. Electrostatics: Gauss’s Law
Negative electric charge 2Q is located on a conducting spherical shell of inner
radius 3.25 a, and its outer radius 4 a. Concentric within the first shell is a
second conducting shell that has -4Q on it. Its inner radius is 1.5 a, and its
outer radius is 2.25 a.
a) Draw E(r) between r=0 and r=8a.
b) Draw V(r) between r =0 and r =8a.
Hint: Divide the problem into appropriate regions of r. Draw the graphs
quantitatively exact – this requires appropriate numbers on the axes. Label
the functional dependence, which each shown curve follows.
6. Point Charges
Consider two point charges which are 4[cm] apart. q1 = + 4[nC] and q2 = - 4[nC].
a) Along the line that connects the two charges, where is the electric field due to
both charges zero?
b) What is the potential due to the two charges at the points which are 3 [cm]
away from q1 and 5[cm] from q2?
7. Electrostatics
Four point charges with charge +2q, -q, +2q, and -2q are arranged as shown (see
figure). The point P is half way between +2q and -2q. If another point charge with
charge –q is located at P, what net force does it feel due to the other four charges
(direction and magnitude)?
Hint: work in multiples of
𝑞
4𝜋𝜀0
and leave r in cm for the calculation
8. Electrostatics: Gauss’s Law
A non-uniform spherically symmetric charge distribution has a charge density
given as follows:
𝑟
𝜌(𝑟) = 𝜌0 ∙ (1 − ) 𝑓𝑜𝑟 𝑟 ≤ 𝑅
𝑅
=0
𝑤ℎ𝑒𝑟𝑒 𝜌0 =
for r > R
3𝑄
>0
𝜋𝑅 3
Obtain an expression for the electric field in the region 𝑟 ≤ 𝑅. Explain your choice
of Gaussian Surface.
Master Equations – Physics 1220
1
𝐹=
4𝜋𝜀0
∙
|𝑞1 |∙|𝑞2 |
1
4𝜋𝜀0
𝐶 ≡
𝑄
𝑉𝑎𝑏
𝑈=
𝑄2
2𝐶
𝐼=
𝑑𝑄
𝑑𝑡
𝜌=
𝐸
𝐽
∑i
=
qi
ri
and V =
𝐶 𝑉2 =
𝑞0

𝜀0
𝑎𝑛𝑑 𝐶𝑝𝑙𝑎𝑡𝑒 = 𝜀0
1
2
𝐹0
𝑄𝑒𝑛𝑐𝑙.
 Φ𝐸 = ∫ 𝐸⃗ ∙ 𝑑𝐴 =
𝑈=
𝑎𝑛𝑑 𝐸⃗ =
𝑟2
1
2
U
q0
𝑎𝑛𝑑 𝐸⃗ = − (𝑖̂
𝐴
𝑑
𝑎𝑛𝑑, 𝑖𝑛 𝑠𝑒𝑟𝑖𝑒𝑠,
𝑄 𝑉 𝑎𝑛𝑑 𝑢 =
1
2
𝜕𝑉
𝜕𝑥
+ 𝑗̂
1
𝐶𝑒𝑞
𝜕𝑉
𝜕𝑦
+ 𝑘̂
𝜕𝑉
)
𝜕𝑧
1
= ∑𝑖 𝐶 , 𝑎𝑛𝑑, 𝑖𝑛 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙, 𝐶𝑒𝑞 = ∑𝑖 𝐶𝑖
𝑖
𝜀 𝐸2
= 𝑛 |𝑞| 𝑣𝑑 𝐴 𝑎𝑛𝑑 𝐽 = 𝑛 𝑞 𝑣𝑑
𝑎𝑛𝑑 𝑉 = 𝐼𝑅 𝑤𝑖𝑡ℎ 𝑅 = 𝜌
𝑃 = 𝑉𝑎𝑏 ∙ 𝐼 = 𝐼 2 𝑅 =
𝐿
𝐴
2
𝑉𝑎𝑏
𝑅
𝑅𝑒𝑞 = ∑𝑖 𝑅𝑖 (𝑠𝑒𝑟𝑖𝑒𝑠)
1
𝑅𝑒𝑞
= ∑𝑖
1
𝑅𝑖
(𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙)
𝐾𝑖𝑟𝑐ℎℎ𝑜𝑓𝑓 𝑅𝑢𝑙𝑒𝑠 ∑ 𝐼 = 0 (𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑟𝑢𝑙𝑒), ∑ 𝑉 = 0 (𝑙𝑜𝑜𝑝 𝑟𝑢𝑙𝑒)
𝑡
𝜀
𝑡
Capacitor charging 𝑞 = 𝑄𝑓 ∙ (1 − 𝑒 −𝑅𝐶 ) 𝑎𝑛𝑑 𝑖 = 𝑅 ∙ 𝑒 −𝑅𝐶
𝑘=
1
4𝜋𝜀0
= 9 ∙ 109 [
𝑁𝑚2
𝐶2
]
Need to take your mind off the exam for a minute? Check these out:
So, there was this mathematician, physicist, and biologist who went into this building and
counted to make sure it was empty, because it was set to be demolished.
So they finish up and count and there is nobody inside. They go across the street and wait. After
some time, two people enter. A few more minutes pass and three people exit.
The physicist says “We must have miscounted”. The biologist says “They must
have reproduced when they were in there”. The mathematician says “Alright,
when one more person enters the building will be empty.
A man, complaining of headaches, entered a hospital for diagnostic tests. A doctor examined the results
for a brain scan and told the patient, "I have bad news and good news for you. The bad news is that you
have a serious brain disease and will die without treatment. The good news is that this hospital has
developed a new procedure for brain transplants and due to a car accident this morning two 'fresh'
brains are available: one is from a taxi driver and the other is from a scientist. The brain of the taxi driver
costs $225,000, while that of the scientist is only $29.95." Puzzled, the patient asked, "Why is the
scientist's brain was so much cheaper?" The doctor replied, "It's used."
Q: What is an electrician's favorite ice cream flavor?
A: Shock-o-lot!
Q: Why are electricians always up to date?
A: Because they are "Current specialists".
Q: How do you pick out a dead battery from a pile of good ones?
A: It's got no spark!
"The good Christian should beware of mathematicians and all those who make empty prophecies. The
danger already exists that mathematicians have made a covenant with the devil to darken the spirit and
confine man in the bonds of Hell." — Saint Augustine.