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Te Test 3 October 14, 2018 PHYS 241-1 hook. Do all work in the examination 7 21. The internal 1. Consider the schematic shown int gure i The baie a nce of each battery is 2.00 (“Ihe capacitor ha: \ ree of 10.0 [Hand is fully charged. Assume re: cap three significant figures for all data Find the loop currents 1; and 1), (You may use any | by hand, If legitimate method to calculate 1) and 1p a you obtain a minus sign explain why. Show work.) Figure | (23 points) round to be zero volts, find the electric b. Taking / potential at the junction directly above resistor R3. (15 points) Find the charge on the capacitor, (Note: The answer is not 120 WC.) (10 points) sistor 2 ‘ A resistor R, an open switch Sand a capacitor C with initial charge qo 4 are connected in series as shown in Figure 2, At time ¢= 0 the switch S Figure 2 is closed, Use Kirchhoff’ sloop rule to set up an initial value problem for the charge q on the capacitor as a a. function of time. (10 points) b. Solve the initial value problem you stated in part a for the charge q on the capacitor as a function of time. (You may use any legitimate method.) (1 2 points) 7 GE ows i Cities . Why is this answer negative? (10 points) a formula for the time constant Lf this circuit. c. Show that the current in this circuit is given b d. Sketch two graphs: one for q vs f and one for i vST- Show wher t= each of your graphs and state the significance in terms of charge and current. (10 points) Do either problem 3 or problem 4 below. If you do both you will receive extra credit. 3. A thin, nonhomogeneous resistor of length Z and uniform cross-sectional area A is shown placed along the x-axis in Figure 3. The resistivity of this resistor varies with position along the x-axis by the formula b is aconstant with units m™.) . + a . L to show that the resistance R of this resistor isiR Use calculus to show ire This segment has resistance dR , resistivity [@), length dx and cross-sectional area A. (Hint: See Figure 3.) Show work. (10 points) ¥ 
