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we drew. If we cross a resistor against the direction of the arrows, the voltage rises by IR. Further, if our loop crosses a battery in the wrong direction—entering in the positive terminal and coming out the negative terminal—the voltage drops by V. To summarize: • Voltage drops by IR when the loop crosses a resistor in the direction of the current arrows. • Voltage rises by IR when the loop crosses a resistor against the direction of the current arrows. • Voltage rises by V when the loop crosses a battery from the negative terminal to the positive terminal. • Voltage drops by V when the loop crosses a battery from the positive terminal to the negative terminal. Let’s now put the loop rule to work in sorting out the current that passes through each of the three resistors in the diagram we looked at earlier. When we looked at the junction rule, we found that we could express the current from A to B—and hence the current from E to D to A—as , the current from B to E as , and the current from B to C—and hence the current from C to F to E—as – . We have two variables for describing the current, so we need two equations in order to solve for these variables. By applying the loop rule to two different loops in the circuit, we should be able to come up with two different equations that include the variables we’re looking for. Let’s begin by examining the loop described by ABED. Remember that we’ve labeled the current between A and B as and the current between B and E as . Because the current flowing from E to A is the same as that flowing from A to B, we know this part of the circuit also has a current of . Tracing the loop clockwise from A, the current first crosses and the voltage drops by . Next it crosses and the voltage drops by . Then the current crosses , and the voltage rises by 12 V. The loop rule tells us that the net change in voltage is zero 234
across the loop. We can express these changes in voltage as an equation, and then substitute in the values we know for , , and : Now let’s apply the loop rule to the loop described by BCFE. Tracing the loop clockwise from B, the arrows cross , but in the wrong direction, from positive to negative, meaning that the voltage drops by 8 V. Next, the current crosses , with an additional voltage drop of . Finally, it crosses , but in the opposite direction of the arrows, so the current goes up by . Now we can construct a second equation: Plugging this solution for into the earlier equation of 4 + 3 = 12, we get: So the current across is 28/13 A. With that in mind, we can determine the current across and by plugging the value for into the equations we derived earlier: 235
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SATII PHYSICS (FROM SPARKNOTES.COM)
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The Good • Because SAT II Subject
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Which SAT II Subject Tests to Take
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After grumbling, however, you still
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Waves 15-19% 11-15 Waves 10% 7-8 Op
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negative, so E, and not A, is the c
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including them anyway because it’
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Two positively charged particles, o
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will a visual representation reliev
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Physics Hint 6: Be Flexible Knowing
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There are a number of ways to label
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Adding Parallel Vectors If the vect
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The result of multiplying A by c is
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neither parallel nor perpendicular.
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Suppose the hands on a clock are ve
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Vector Addition Practice Questions
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2. A The vector 2A has a magnitude
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path, Alan has traveled a much grea
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school student called Andrea. Andre
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centimeters to the left of its star
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We can learn two things about the a
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Acceleration vs. Time Graphs After
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The variable represents the object
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Note that there are certain conveni
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1. . An athlete runs four laps of a
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10. . A woman runs 40 m to the nort
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We know the total distance the spri
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Principles of Natural Philosophy. I
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The component form of Newton’s Se
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e in the direction. And since the s
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which reflects its resistance to be
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In the diagram above, the weight an
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A student pushes a box that weighs
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1. . Each of the figures below show
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7. . In the figure above, a person
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Since the block is motionless, the
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When we are told that a person push
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EXAMPLE A water balloon of mass m i
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The graph above plots the force exe
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Though energy is always measured in
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there is a negative amount of work
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smallest. The answer to question 3
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Mechanical Energy Average Power Ins
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to a height of 8 m over a time of 4
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8. C When the book reaches the pers
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determining what those right number
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the ground. The system is initially
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calculators, you almost certainly w
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and minimize M.” With such a ques
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2. WHAT IS THE ACCELERATION OF THE
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Adding these two equations together
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force of friction: . Using Newton
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m, placed on a frictionless surface
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Frequency is given in units of cycl
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of the spring due to the gravitatio
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The oscillation of a pendulum is mu
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Velocity Calculating the velocity o
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Practice Questions 1. . Two masses,
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7. . An object of mass 3 kg is atta
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Since the system is in equilibrium,
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velocity, v. Linear momentum is den
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Conservation of Momentum If we comb
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As we might expect, the final veloc
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A pool player hits the eight ball,
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two-dimensional collision is effect
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For a System of Two Particles For a
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At the front end of the boat, the f
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4. . A scattering experiment is don
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1. B The athlete imparts a certain
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7. E Momentum is conserved in this
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The diver’s translational motion
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30 π/6 45 π/4 60 π/3 90 π/2 180
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elative position to one another. As
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acceleration given its angular velo
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To find the direction of a rigid bo
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A student exerts a force of 50 N on
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The torque that produces the angula
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The masses in the figure above are
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an object sliding down a frictionle
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Velocity Average Angular Accelerati
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3. . What is the direction of the a
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1. D An object that experiences 120
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At the top of the incline, the disk
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from a Latin word meaning “center
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Newton’s Law of Universal Gravita
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when you are beneath the surface of
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EXAMPLE A satellite of mass is laun
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Kepler’s Laws After poring over t
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Practice Questions Questions 1-3 re
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8. . A satellite orbits the Earth a
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Circumference and radius are relate
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Page 187 and 188: Just as specific heat tells us how
Page 189 and 190: Conduction is the transfer of heat
Page 191 and 192: Effectively, this equation tells us
Page 193 and 194: the way that it does. The Laws of T
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Page 197 and 198: If we know our formulas, this probl
Page 199 and 200: 5. . An ideal gas is enclosed in a
Page 201 and 202: Asphalt, like most materials, has a
Page 203 and 204: The things we call atoms today are
Page 205 and 206: If they come up on SAT II Physics,
Page 207 and 208: will move in the opposite direction
Page 209 and 210: Work The work done to move a charge
Page 211 and 212: Much like gravitational potential e
Page 213 and 214: 3. . A particle of charge +2q exert
Page 215 and 216: 7. . A particle of charge +q is a d
Page 217 and 218: The vector sum of the three vectors
Page 219 and 220: Voltage The batteries we use in fla
Page 221 and 222: This equation tells us that we can
Page 223 and 224: If the two variables you know are a
Page 225 and 226: However, each resistor causes a vol
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Page 229 and 230: Consider again the circuit whose to
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Page 237 and 238: capacitance is halved. The proporti
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Page 241 and 242: 4. . Two resistors, and , are ident
Page 243 and 244: 10. . A dielectric is inserted into
Page 245 and 246: The equivalent capacitance of two c
Page 247 and 248: The Earth itself acts like a huge b
Page 249 and 250: Because the velocity vector and the
Page 251 and 252: A particle with a positive charge o
Page 253 and 254: The constant is called the permeabi
Page 255 and 256: 1. . The pointer on a compass is th
Page 257 and 258: 7. . A positively charged particle
Page 259 and 260: 1. B To solve this problem, it is h
Page 261 and 262: If the particle is to move at a con
Page 263 and 264: flowing in the counterclockwise dir
Page 265 and 266: Next, let’s calculate the flux th
Page 267 and 268: Remember that field lines come out
Page 269 and 270: Magnetic Flux Faraday’s Law / Len
Page 271 and 272: 5. . A wire carrying 5.0 V is appli
Page 273 and 274: In this equation, A is the amplitud
Page 275 and 276: Ernst attaches a stretched string t
Page 277 and 278: A string is tied to a pole at one e
Page 279 and 280: other. The principle of superpositi
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Page 283 and 284: The Doppler Effect So far we have o
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Practice Questions 1. . Which of th
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6. . Two pulses travel along a stri
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1. B Simple harmonic motion is defi
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where and are the frequency heard b
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A higher frequency—and thus a sho
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The phenomenon of refraction result
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Since we know that the ratio of / i
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The four basic kinds of optical ins
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You can test all this yourself with
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Because is a positive number, we kn
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As the diagram shows us, and as the
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At any point P on the back screen,
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Note that the pattern is brightest
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One of the more common ways of test
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3. . When the orange light passes f
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9. . Sound waves do not exhibit pol
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7. E Only concave mirrors and conve
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For people who believed that light
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What does this all mean? Time is re
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A spaceship flying toward the Earth
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Rutherford’s Gold Foil Experiment
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The Wave Theory of Electromagnetic
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The Problem with Rutherford’s Mod
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Don’t worry: you don’t need to
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A hydrogen atom is energized so tha
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where is the uncertainty in a parti
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electrons have mass, it is so negli
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chapters on mechanics are the resul
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You won’t need to calculate the n
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Photoelectro n Radius of Electron O
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5. . An electron is accelerated thr
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according to the formula , where l
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In radioactive substances, the numb
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A scale for measuring temperature,
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The points of maximum displacement
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Electromagnetic spectrum The spectr
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The amount of time it takes for one
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Given the period, T, and semimajor
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The substance that is displaced as
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A back-and-forth movement about an
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Refracted ray Refraction Restoring
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T Tail Tangent A body or set of bod
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Weber Weight The force involved in
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pinpointing what you need to study
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If you got a question wrong because
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