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mat-sln-asn-hwk19-spr02

# mat-sln-asn-hwk19-spr02 - Solution for Homework 19 RL...

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Solution for Homework 19 RL Circuits Solution to Homework Problem 19.1(Resistance Given Time Constant) Problem: A RL circuit has a time constant, τ , of 40s and an inductance, L, of 3H what is the resistance of the circiut? Select One of the Following: (a) 0 (b-Answer) 0 . 075Ω (c) 10Ω (d) 26Ω (e) 42Ω Solution The time constant for a RL circuit is defined by, τ = L R solve for R, R = L τ sustitute, R = 3 H 40 s evaluate, R = . 075Ω Total Points for Problem: 3 Points Solution to Homework Problem 19.2(Long/Short RL Problem) Problem: A coil of resistance 12Ω and self-inductance 2mH is connected across an ideal 12V battery. (a)What is the initial current? Select One of the Following: (a-Answer) 0A (b) 1A (c) 144A (d) 0 . 024A (e) 6000A (b)What is the final current? Select One of the Following: 1

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(a) 0A (b-Answer) 1A (c) 144A (d) 0 . 024A (e) 6000A Solution to Part(a) When the circuit is first connected, the inductor allows zero initial current flow, I (0) = 0 , since an inductor resists changes in current and does not allow instantaneous changes in current. Grading Key: Part (a) 2 Points Solution to Part(b) After a long time, I is not changing, so Δ V L = dI dt = 0 , and substituting into the loop equation, Δ V battery - IR = 0 , gives I = Δ V battery R = 1 A. Grading Key: Part (b) 2 Points Total Points for Problem: 4 Points Solution to Homework Problem 19.3(Magnetic Field of Two WIres) Problem: Two infinite straight wires carry current I = 2A as shown below. One wire is parallel to the y axis and one wire is parallel to the z axis. The current directions are as drawn. The distance from each wire to point P is 3cm . Calculate the magnetic field at point P . Be sure to report the magnetic field as a vector. Select One of the Following: (a) 2 . 4 × 10 - 5 Tˆy + 2 . 4 × 10 - 5 z (b) 1 . 3 × 10 - 5 Tˆx - 1 . 3 × 10 - 5 Tˆy (c) 2 . 4 × 10 - 5 Tˆy - 2 . 4 × 10 - 5 z (d-Answer) 1 . 3 × 10 - 5 Tˆy - 1 . 3 × 10 - 5 z (e) 0 2
I d d x y I P Wire 1 Wire 2 Solution (a) The field of an infinite wire: The field of on infinite wire is given by B = μ 0 I 2 πR R is the same for both wire one and wire two. The direction can be read off using the right-hand rule. (b) Compute the field of wire one: vector B 1 = μ 0 I 2 πR = (4 π × 10 - 7 Tm A )(2A) 2 π (0 . 03m) = 1 . 3 × 10 - 5 Tˆy (Correct Sig Figs) (c) Compute the field of wire two : vector B 2 = μ 0 I 2 πR = (4 π × 10 - 7 Tm A )(2A) 2 π (0 . 03m) = - 1 . 3 × 10 - 5 z (Correct Sig Figs) (d) Compute the total field: The total field is the vector sum of the two vector B tot = vector B 1 + vector B 2 = 1 . 3 × 10 - 5 Tˆy - 1 . 3 × 10 - 5 z Total Points for Problem: 3 Points Solution to Homework Problem 19.4(Velocity of Alpha Particle) 3

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Problem: An alpha particle is a Helium nucleus and has twice the charge, q = 2 q p , and four times the mass, m = 4 m p , of a proton (the mass of a proton is m p = 1 . 67 × 10 - 27 kg and the charge of a proton is q p = +1 . 6 × 10 - 19 C ).
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