PHYSICS 2213 Homework 5 DC Circuits Due Monday, July 11. Learning Goals: By the time this homework is due, your studying should enable you to: o Relate magnitudes and directions or polarities of electric currents, voltages, and electric lields in electric circuits. 0 Sketch a graph for electric potential as a function of position in an electric circuit (Without doing detailed numerical calculations). 0 Where possible, reduce networks of electrical resistances to simpler equivalent forms using series and parallel resistance combinations. Recognize when this reduction isn't possible. 0 Determine the power dissipated by electrical resistances (including light bulbs) in circuits. 0 Predict how properties of electric circuits will change when components or connections are changed. 0 Explain how electrical resistivity and resistance of dierent materials depend 011 temperature conduc- tors, semiconductors, superconductors. 0 Show that algebraic and numerical results have correct units and are physically reasonable. Questions and Problems from the 13th ed: Chapter 26, Questions Q26.4, Q26.9, Q2613, Q2618. Chapter 26, Excersises & Problems 1, 5, 13, 26, 74. Question 1. Voltage Divider. | A common electric circuit is the voltage divider shown here. Its purpose is to access a specied fraction of a source voltage, in this case the EMF 5 of an ideal power supply (no internal r). (a) What circuit quantity is the same for the two resistors? Why? (b) What is the voltage Vde between output terminals d and e (in terms of a)? What fraction is this of the battery EMF .5? Show that your algebraic result is physically reasonable by considering appropriate limiting cases for R1 and R2. (c) What happens to voltage Vde when a load resistance Rload such as a light bulb is connected across terminals d and e? Under what condition on Bload compared to R1 and/or R2 would Vde not differ much from its value in part (a)? Please give your reasoning. Question 2. Current Divider. In this circuit the current through the power supply and resistor R1 divides between resistors R2 and R3 . The power supply is ideal (no internal resistance). (a) What circuit quantity is the same for R2 and R3? Why? (b) Show that the electric currents [2 and [3 in resistors R2 and R3 are inversely proportional to those resistances. Please be sure your reasoning is clear. ((3) Write an expression for the equivalent resistance of resistors R2 and R3 . What values does this equivalent resistance take when R3 > oo (\"opencircuit\") and when R3 > O (\"shortcircuit\")? What are the currents through R1, R2, and R3 in each of these limiting cases? (cl) Why is each of the special limiting values of current you found in (c) physically reasonable? Why are the nicknames \"shortcircuit\" and \"opencircuit\" appropriate for these two cases? How could you achieve each of these limiting cases in the circuit without using resistor R3? You may use other wires if you wish. Question 3. Five Lamp Circuit. All the light bulbs are identical, and the power supply is ideal (no internal r). (a) Rank the bulbs in order of brightness from dimmest to brightest. Please give your reasoning. (b) If one bulb were removed from the circuit, leaving two disconnected wire ends, what would happen to each remaining bulb? Consider removing each bulb separately. Please give your reasoning. (c) If an ideal wire were connected across one bulb, what would happen to each remaining bulb? Consider doing this to each bulb separately. Please give your reasoning