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Unformatted text preview: Solution for Homework 19 RL Circuits Solution to Homework Problem 19.1(Current in an LR Circuit) Problem: After the switch in the circuit in the figure is closed Select One of the Following: (a) The current in the circuit is zero at one time constant later. (b) The current is zero for a long time after the the switch is closed but eventually reaches I max . (c) The current is I max immediately after the switch is closed. (dAnswer) The current I max occurs a long time af ter the switch is closed. Solution The current in an L R circuit increases in time reaching its maximum current a long time after the circuit is completed. Thus, choice (d) is correct. Total Points for Problem: 3 Points Solution to Homework Problem 19.2(Charging the Sewer Pipe Solenoid) Problem: Our sewer pipe solenoid (OK everyone knew this was going to be here) is wound with 79 turns over 79cm . The radius of the sewer pipe is 5 . 5cm . It is connected to a cruddy battery with internal resistance . 6Ω . How long does it take the battery to charge the solenoid to 99% of the solenoid’s final current? Select One of the Following: (a) 1 . 6 × 10 4 s (b) 3 . 3 × 10 2 s (c) 61s (dAnswer) 7 . 2 × 10 4 s (e) 9 . 1 × 10 6 s Solution (a) Compute the Inductance: The inductance of a solenoid in the infinite solenoid approximation is L = n 2 μ Aℓ = parenleftbigg N ℓ parenrightbigg 2 μ πR 2 ℓ = parenleftbigg 79 . 79m parenrightbigg 2 (4 π × 10 7 Tm A ) π (0 . 055m) 2 (0 . 79m) L = 9 . 43 × 10 5 H 1 (b) Compute the Time Constant: The time constant for an RL circuit is τ = L R = 9 . 43 × 10 5 H . 6Ω = 1 . 57 × 10 4 s (c) Calculate the Decay Time: The current is increasing from zero to its final value I f , so the time dependence of the current is I ( t ) = I f (1 e t τ ) The time to reach 99% of the full current is . 99 = I ( t 99 ) I f = 1 e t 99 τ e t 99 τ = 0 . 01 Take the log of both sides ln(0 . 01) = t 99 τ So the time to reach 99% of the final current is t 99 = τ ln(0 . 01) = (1 . 57 × 10 4 s)( 4 . 61) = 7 . 2 × 10 4 s Total Points for Problem: 3 Points Solution to Homework Problem 19.3(Torque on Two Permanent Alnico Magnets) Problem: Two cubic Alnico permanent magnets are 10cm apart. The length of one side of the magnets is 1cm . Compute the magnitude of the maximum torque one magnet can exert on one another. You will have to look up the magnetization density in the course readings. Select One of the Following: (a) 1 × 10 2 Nm (b) 5 × 10 2 Nm (c) 3 × 10 3 Nm (d) 7 × 10 4 Nm (eAnswer) 2 × 10 4 Nm Solution (a) Compute the Magnetic Moment: The magnetization density of Alnico is M = 0 . 995 × 10 6 A / m . The total magnetic moment is the magnetization density multiplied by the volume m = MV = Mℓ 3 = (0 . 995 × 10 6 A / m)(0 . 01m) 3 = 0 . 995Am 2 m m 2 (b) Compute the Magnetic Field: The magnetic field of a dipole is strongest in the direction of the dipole moment. The magnitude of the magnetic field of a dipole at a distancemoment....
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This note was uploaded on 05/04/2008 for the course PHYS 2074 taught by Professor Stewart during the Spring '08 term at Arkansas.
 Spring '08
 Stewart
 Physics, Current, Work

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