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# s61 - Solutions to Homework#6 Chapter 23 50 Picture the...

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Solutions to Homework #6 Chapter 23 50. Picture the Problem : A solenoid has 640 turns, is 24 cm long, and has a radius of 4.3 cm. Strategy: Solve equation 23-14 for the inductance. Solution: Calculate the inductance: ( 29 ( 29 2 2 2 7 0 640 4 10 T m/A 0.043 m 12 mH 0.25 m N L A μ π π - = = = �� l Insight: To double the inductance, you could increase either the radius or the number of turns by 2 , or you could cut the length in half while keeping the number of turns the same. 54. Picture the Problem : The four electrical circuits shown in the figure at the right have identical batteries, resistors, and inductors. Strategy: A long time after the switch is closed each inductor will act like an ideal wire. Use this principle and the rules of adding resistors in series and in parallel to determine the ranking of the currents supplied by the batteries. Solution: Let each battery have emf ε and each resistor have resistance R . For circuit A the inductor will act like an ideal wire when the switch has been closed for a long time, and the current supplied by the battery will be . R ε For circuits B and C the resistors in parallel with the inductor are shorted out, and make no contribution to the current in the circuit. The current supplied by the battery in those circuits is also . R ε For circuit D the equivalent resistance of the two resistors in parallel is 2, R so the current supplied by the battery after a long time, when the inductor acts as an ideal wire, is 2 . R ε The ranking of the currents, therefore, is A = B = C < D. Insight: While inductors act like ideal wires in DC circuits, capacitors act like open switches (see Chapter 21). If each inductor were replaced by a capacitor, the currents in each circuit would be A, zero; B, 2 ; R ε C, 2 3 ; R ε and D, zero. 58. Picture the Problem : The number of turns per meter in a solenoid of fixed length is doubled. At the same time, the current in the solenoid is halved. Strategy: Use equations 23-14 and 23-19 to determine the effect of the described changes on the energy stored in the solenoid.

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