Physics 42 Exam 2 PRACTICE Name: Lab 1 2 3 4 Conceptual Multiple Choice (2 points each) Circle the best answer. 1.Rank in order, from brightest to dimmest, the identical bulbs A to D. A. C = D > B > A B. A > C = D > B C. A = B = C = D D. A > B > C = D E. A > C > B > D 2. In a discharging RC circuit, it takes one time constant for the capacitor to discharge completely. A) TRUE B) FALSE 3. The resistors are identical. What is the direction of the current in the circuit? A. clockwise B. counterclockwise C. zero 4. A copper wire of length L and radius b is attached to another copper wire of length L and radius 2b, forming one long wire of length 2L. This long wire is attached to a battery, and a current is flowing through it. Relative to the electric field within the wire of radius b, the magnitude of the electric field within the wire of radius 2b is A) four times weaker. B) four times stronger. C) two times weaker. D) two times stronger. E) equal. 5. A current flowing through a copper wire (which is connected to a battery) is due to A) electrons being accelerated by an electric field. B) positively charged particles being pushed off the battery terminal. C) electrons being bumped by positively charged particles. D) positively charged particles being attracted to the negative terminal of a battery. 6. A parallel plate capacitor of capacitance C 0 has plates of area A with separation d between them. When it is connected to a battery of voltage V 0, it has charge of magnitude Q 0 on its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the capacitance of the capacitor and the magnitude of the charge on the plates are 1 1 a. C0, Q0 2 2 1 b. C0, Q 0 2 c. C 0, Q 0 d. 2C 0, Q 0 e. 2C 0, 2Q 0
Problems. Show ALL the work for any credit. BOX final answers. NEATNESS COUNTS. Report final answers to 3 significant figures in decimal form or using scientific notation. 1. (10 points) If the magnitude of the drift velocity of free electrons in the copper wire is 7.84 10 4 m/s, what is the 28 3 current? The electron density in the wire is 8.49 10 m. The diameter and length of the wire are 0.50mm and 2.50m, respectfully. 2. (10 points) A dipole centered at the origin with moment 5.0 μc m is oriented at an angle of π/6 with respect to the x-axis. The positive charge is in the first quadrant. An electric field points in the positive x direction and has a magnitude of 9.0 10 6 N/C. Find the torque the electric field exerts on the dipole. Sketch the situation.
3. (20 points). C 1 = 20 µf, C 2 = 10 µf, C 3 = 30 µf, and ΔV = 10V. a. Find the equivalent capacitance of the circuit shown. BOX IT. b. When fully charged, find the charge on each capacitor, the voltages and the energy stored in each capacitor. Put your results in the table. c. Is energy conserved? Show it. Explain it. Equivalent Capacitance: C (µf) V(V) Q (C) U (J) 20 10
30 4. (20 points) In the RC circuit shown the switch has been on point a for a long time so that the capacitor is fully charged. The switch is then moved to position b and the capacitor discharges. NO DERIVATIONS REQUIRED. BOX EVERYTHING. a. What is the initial charge and voltage of the capacitor? b. Calculate the time constant for the circuit when it discharges. c. Find the time for the capacitor to discharge half way. d. Find the current across through the resistor at that time.
5. (20 points) For the circuit shown find the following. Assume the voltage supplies are ideal. Use three sig figs and report answers decimals. a) Apply Kirchhoff s Rules to the circuit to generate equations for the circuits. Redraw the circuit labeling the currents and the directions of the currents you select. Show an equation for each unknown, etc. Show your work! Then if you use a rref matrix to solve the system of equations, show that or else show the algebra. You do not need to show work for multiplying across the table to get V and P. b) Find the voltage across and power dissipated by each resistor. Put your results in the table. c) Find the total power delivered by the two emf sources. Is energy conserved? Explain. You might need to keep more digits to show this. R (Ω) I (A) V (V) P (W) 5.0 8.0 10.0 Totals
Extra Credit. (10 points) A coaxial cable has a capacitance of 3.0 pf. The inner conductor has a radius of 1.0 mm, and the outer conductor has an inner radius of 1.5 mm. Find the length of the cable. Justify all your steps. This is a derivation. You have to derive the expression for the capacitance in order to find the length. Use diagrams, Gauss s Law, etc. Explain your steps. This is only extra credit because the test is long. This sort of question might also be on the exam!!!!