City Tech - New York City College of Technology PHYS 1442 - General Physics II: Calculus Based. Exam 1 October 3, 2018

Exam 2 Statistics

Problem. PS and PP are rates of energy dissipation in 3 resistors...

Problem

P_S and P_P are rates of energy dissipation in 3 resistors, when they are connected in series and in parallel respectively with some source of constant voltage. Let lowest resistance is known, r, 2^nd resistance is greater then the first on the factor of N. What is the resistance of the 3^rd resistor?
(a) Derive algebraic expression for the second resistance
and then
(b) use this expression to find numerical solution for the following data:
P_S=1 W, P_P=11 W, N=2, r=1Ω.

Solution:

V²/R_P=P_P

V²/R_S=P_S

R is 3^rd resistance.

R_S=r+Nr+R

1/R_P=1/r+1/(Nr) +1/R

R_P=1/( 1/r+1/(Nr) +1/R  )

P_P/P_S =R_S/R_P = R_S·(1/R_P)

P_P/P_S =R_S/R_P = (r+Nr+R)·( 1/r+1/(Nr) +1/R)

P_P/P_S=a

(r+Nr+R) (1/r+1/(Nr)+/R)=a

(1+N+R/r)(1+ 1/N + r/R) = a; Solve for x=R/r

R/r=x

P_P/P_S=a=11

11=(1+2+x)(1+1/2+1/x)

11=(3+x)(3/2+1/x)

11x=(3+x)(1.5x+1)

Solutions: x=3, x=2/3

R/r = 3

R=3·1Ω = 3Ω

What is the resistance...

4. What is the resistance (R) of the resistor if the electric current (I) flowing through this resistor is equal to 2 A, and the electric potential (V_L) on the left terminal of this resistor is 4 V and the electric potential (V_r) on the right terminal of this resistor is 10 V. Which is direction of the electric current through this resistor, toward left or right?
V_r - V_L = ΔV_r,l = -I_r,l R
-I_r,l R = (V_r - V_L )

-I_r,l  = (V_r - V_L )/R

I_r,l  = (V_L – V_r )/R

 R = |(V_L – V_r )/ I_r,l |

R  = |(4V – 10V )/2A| = 3 Ω

The electric current flows from greater potential, 10V, right, to the lower potential, 4V, left: toward to left.

Exam 1. Problem 1

Exam 1. October 8, 2015, 8:00 AM
In solutions students should show:
a) given data by symbols,
b)   the unknown by symbol,
c) useful for this problem general formulae,
d) algebra job and final algebraic expression for the unknown,
e) substitution of symbols in the final algebraic expression by numbers with measurement units,
f) if it is required by a problem the final number with measurement units.

1. Electric field (E) accelerates a charged droplet from the zero speed to the final speed (V₁) of 8 m/s. What will be the final speed (V₂) if the electric field is decreased by a factor of 4, but all other parameters of this accelerator are not changed?

The electric field is decreased by a factor of 4 means: E₂= E/4, E₂/E=1/4

Potential energy of electric field, U=E∙d∙q
Kinetik Energy, K=½mv²

U=K

E∙d∙q = ½mv₁²,
where d is the traveling distance of the droplet in the electric field, q is the droplet’s electric charge.

E₂∙d∙q = ½mv₂²

(E₂∙d∙q)/ (E₁∙d∙q) =  (½mv₂²)/(½mv₁²)

E₂/ E =  v₂²/v₁²

v₂² = v₁² ∙E₂/ E

v₂ = v₁ ∙(E₂/ E)^1/2

v₂ = 8m/s ∙(1/4)^1/2 = 8m/s ∙(1/2) = 8m/s  /2 = 4m/s   

Writing Problem Solutions in Physics Exam

Present your work so that the grader knows what you are thinking.

Just giving “the answer” to a problem without any work will earn you no credit, even if you are correct.

Style

Your problem solution should be written in technical style.

When helpful, present information in the form of idealized diagrams, tables, lists, mathematical derivations, and so forth.

Solution Structure

Diagram

Begin your solution by presenting the situation it describes and all of the information it gives you, i.e., by presenting your understanding of the problem definition. Drawing a picture is usually the most effective (and time efficient — very important on exams) way to do this; incorporate the given information into the picture by labeling it. Turn your picture into a technical diagram reducing the situation to only the physically relevant parts. For example, if our problem were about forces, draw a free-body diagram.

Given and target data

Describe the Physics. Convert the problem that you have described into physics terms.

Define physical variables. Write down given data and target quantity, using variable symbols.

Equations

Write down related equations that you think will be useful. Concretely, it often helps to classify your problem by its method of solution.

Math

Use mathematics to find a symbolic expression giving the target quantity in the terms of the given information.

I don’t ask you to provide textual commentary as you go, narrating what you are doing and explaining anything, as often it is very difficult to read hand-written texts, however you should write out all your steps of mathematical transformations in correct mathematical expressions.

Use logical symbols or short phrases (one - two words) to explain the sequence and the logic of your work. Make your logic clear.

You should use the conventions of physics and mathematics to communicate much information implicitly.

For example, don't explain that g is the acceleration due to gravity, because it is conventional and because of the context.

Solve with symbols first. Do not substitute numerical values into your expressions as you go. Work with symbols.

Substitution

When you have your symbolic solution giving the target quantity in the terms of the given information (expressed by symbols), you can substitute any given (or generally known ones, like g) numerical values with appropriate measurement units into your symbolic solution to find a numerical solution with measurement units. 

Show transformations with measurement units. Give prove that your symbolic solution give correct units of the target quantity. 

This part will not be present for problems that don’t provide numerical values.

Report

Write separately and highlight final numerical value. Report numbers with units specified and with reasonable significant figures.

Main Sections

So, main sections of your solution:

1. Diagram

2. Given and target data

3. Equations

4. Math (Math transformations to find a symbolic solution)

5. Substitution (Substitutions of numerical physical values into the symbolic solution)
6. Report

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