Physics 4B Winter 2018 Test 2

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1 Physics 4B Winter 018 Test Name: Feb 15, 018 Please show your work! Answer as many questions as you can, in any order. Calculators are allowed. Books, notes, and internet connected devices are not allowed. Use any blank space to answer questions, but please make sure it is clear which question your answer refers to. When asked for an expression, give your answer only in terms of the variables given in the question and fundamental constants such as g, k, e, and so on. DO NOT OPEN TEST BOOKLET UNTIL TOLD TO DO SO. g = 9.8 ms k = Nm C = 1 4πɛ 0 ɛ 0 = C N 1 m e = C m e = kg m p = kg C = πɛ 0 L ln(b/a) ab C = 4πɛ 0 b a ρ ρ 0 = αρ 0 (T T 0 ) Trigonometric Identities sin θ + cos θ = 1 sin(θ) = sin(θ) cos(θ) cos(θ) = cos θ sin θ sin(α ± β) = sin α cos β ± cos α sin β cos(α ± β) = cos α cos β sin α sin β cos α cos β = 1 [cos(α β) + cos(α + β)] sin α sin β = 1 [cos(α β) cos(α + β)] sin α cos β = 1 [sin(α + β) + sin(α β)] sin ( θ + π ) = cos θ cos ( θ + π ) = sin θ sec θ := 1 cos θ csc θ := 1 sin θ cot θ := 1 tan θ 1

2 1. A certain copper wire has a resistance of 6.00 Ω at 0.0 C. (a) What resistance will it have at 35.0 C? [4 pts] (b) Suppose the wire connects the terminals of an ideal emf source, and as current passes through it, it heats from 0.0 C to 35.0 C. What is the ratio of the power dissipated as heat in the wire at 35.0 C to the power dissipated at 0.0 C? [3 pts] (At 0.0 C, copper has a resistivity of Ω m and a temperature coefficient of resistivity of ( C) 1.)

3 known to four significant figures. DV/I for DV V to V. Assume I na 76. Review. When a straight wire is warmed, its resistance T 5 80 K, 300 K, and 30 K. S is given by R 5 R 0 [1 1 a(t T 0 )] according to Equation 7.0, consists where a ofis square the temperature plates of edge coefficient lengthof l, that 81. are The separated potential difference acro. A parallel-plate capacitor by a distance d, where resistivity. d This l. expression A potential needs difference to be modified V is maintained if we bulb is maintained at a const between the plates. A material include of dielectric the change constant in dimensions κ fills half of the the space wire due between to rium temperature is being re the plates. The thermal expansion. Find a more precise expression for current in the bulb is only o dielectric slab is withdrawn the resistance, from one the that capacitor includes the as shown. effects of changes drawn by the bulb when it is fi in the dimensions of the wire when it is warmed. Your perature coefficient of resistiv (a) What is thefinal charge expression on theshould capacitor be in terms after the of R dielectric is completely is withdrawn? [ pts] temperature coefficient of resistivity a, and the coef- with increasing temperature, ( C) 1 and the resi 0, T, T 0, the ing temperature of the filame (b) What is the ficient charge of linear on the expansion capacitor a9. initially, when the dielectric fills half the space between 77. Review. the plates? A parallel-plate [4 pts] capacitor consists of square Challenge Problems S (c) Find the capacitance plates of edge whenlength the left, that edgeare of separated the dielectric by a is distance d, where d,,,. A potential difference DV is at a 8. distance A more x general from definition of the center of the capacitor. [3 pts] S cient of resistivity is maintained between the plates. A material of dielec- (d) If the dielectric is removed at a constant speed v, what is the current in the circuit a5 1 dr constant k fills half the space between the plates. r dt as the dielectric The dielectric is being withdrawn? slab is withdrawn Which from way the iscapacitor the current as flowing? [4 pts] shown in Figure P7.77. (a) Find the capacitance when where r is the resistivity at tem ing a is constant, show that d x Figure P7.77 S v V r 5 r 0 e a(t where r 0 is the resistivity at te the series expansion e x < 1 1 the resistivity is given approxim r 5 r 0 [1 1 a(t T 0 )] fo 83. A spherical shell with inner ra S r b is formed from a material 3

4 3. In the circuit shown, the reading on the ideal voltmeter is 6.00 V, with point a being the high potential side and point b being the low potential side. A V a V b E V (a) Find E, the value of the ideal emf source. [3 pts] (b) What is the expected reading on the ideal ammeter? [7 pts] 4

5 4. Consider the resistance-capacitance circuit shown. It includes an ideal 10 V battery. Initially the switch is open and the capacitor is uncharged. (a) What is the effective resistance of this arrangement just at the moment the switch is closed? [5 pts] (b) What is the effective resistance of this arrangement after the switch has been closed for a long time? [4 pts] (c) What is the potential difference across the capacitor when the switch has been closed for a long time? [5 pts] (d) After the switch has been closed a long time, it is opened again. Sketch a graph of the potential difference across the capacitor against time after the switch is opened, labelling the axes with the appropriate initial value. [3 pts] S 10.0 V mf Figure P8.43 5

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PHYSICS 7B, Section 1 Fall 2013 Midterm 2, C. Bordel Monday, November 4, pm-9pm. Make sure you show your work!

PHYSICS 7B, Section 1 Fall 2013 Midterm 2, C. Bordel Monday, November 4, 2013 7pm-9pm Make sure you show your work! Problem 1 - Current and Resistivity (20 pts) a) A cable of diameter d carries a current