Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Physics 251 Test Review 2 (12th edition) Test 2 covers Chapters 23-30 of the text. There is a small amount of overlap with Test 1, especially Chapter 22. * Capacitance calculations (Chapters 23, 24) Step 1: calculate the electric field (E) from Gauss’ Law Step 2: calculate the voltage difference between surfaces using V = Edl Step 3: find capacitance from C = Q/V surface text references/examples of steps 1,2,3: Step 1 Step 2 infinite plane cylinder sphere * * Ex. 22.8, p.765 Ex. 22.6, p.763 Ex. 22.5, p. 762 Ex. 23.9, p.796 Ex. 23.10, p. 797 Ex. 23-8 p795 Step 3 p.817 Ex. 24-4, p. 819 Ex. 24-3, p. 819 capacitor with dielectric constant, page 850ff Resistivity of a rod (Ch. 25); see ,for example, Example 25-4, page 856 Direct Current circuits - capacitors in series and parallel (compute charge, voltage, equivalent capacitance) - resistors in series and parallel (compute current, voltage, equivalent resistance) - Kirkhoff’s Laws, junction and loop equations * magnetic field from a current density, Ampere’s Law (Section 28-7) * electromagnetic induction, slide wire * LRC circuits (D.C. only) * charged particle motion; vector cross product (Section 27-4) Copyright 2008, John R. Newport, Ph.D. 1 Problem 1 Consider the circuit shown below. The Ri represent resistors. The gray highlighted letters identify connection points. ε is an ideal voltage source. E A ^^^ R1 C F ^^^ R2 ^^^ R3 B ^^^ R4 ^^^ R5 D | |ε| | a.) Identify the number and location of each of the items below. Assume that the resistances and source voltage are known. Use the gray highlighted letters. Identify voltage drops across resistor Ri as Vi. - How many nodes are there in this circuit? Where? ________________________ - How many loops possible? Where? ________________________ ____________________________________________________________ - How many current variables are there? ________________________ - Is this system solvable? (i.e., can you solve ________________________ for all of the currents?) Why? Copyright 2008, John R. Newport, Ph.D. 2 b.) Set up the loop and node equations using Kirkhoff’s Laws (but do not solve them). Clearly identify the node or loop, including all directions, associated with each equation. DRAW EACH CURRENT ON THE DIAGRAM ABOVE, CLEARLY SHOWING ITS DIRECTION! Use the gray highlighted letters. Identify voltage drops across resistor Ri as Vi. (For example, the voltage drop across R1 is V1.) c.) What is the algebraic method used for solving this system? (name?) Copyright 2008, John R. Newport, Ph.D. 3 Problem 2 A cylindrical conductor (radius R) has current flowing in the direction of its axis. a.) The current density is J(r) = Ae-(r/R). Find A in terms of the total current, I0. (Use the definition of J.) Hint: xexdx = xex - ex b.) What is the magnetic field within the conductor, 0<r<R? c.) What is the magnetic field outside of the conductor, r>R? d.) What is the principle (law) used in these calculations? Copyright 2008, John R. Newport, Ph.D. 4 Problem 3 A slide wire (resistance R) travels without friction along the track shown below. It starts from position x0 (non-zero) and velocity v0 , to the right as shown. Assume that the v shaped rails meet at an angle of . Use the coordinate system shown. The magnitude of the external magnetic field is constant. The direction of the external magnetic field is also constant (into the page). y xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx x x x x x x x x x x x x v0 x a.) State the principle that describes how to calculate the magnitude of the motional electromotive force (this can be an equation). b.) State the principle that describes how to compute the direction of the current associated with the electromotive force. (words) c.) Write the equation of the area enclosed in terms of x only. (Hint: What is the equation of the slanted line? Write the slope in terms of .) d.) Find the induced electromotive force. This will be a function of both x(t) and v(t). e.) What is v(t)? (Algebraic equation for v(t).) Copyright 2008, John R. Newport, Ph.D. 5