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# capa11 - Solution Derivations for Capa#11 Caution The...

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Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5 . 0 V , R = 155 Ω, L = 8 . 400 × 10 - 2 H . In the diagram above, what is the voltage across the inductor in the instant just after the switch is closed? V b = Given R = Given L = Given From Kirchhoff’s Loop law, we can get an equation for the voltages around the circuit. V b - IR - E L = 0 where E L is the EMF of the inductor. Thus, E L = V b - IR Immediately after the switch is closed, there is no current in the circuit. The resistor and inductor are in series, and the inductor opposes the change in current. Thus, there is no voltage drop across the resistor and the voltage drop across the inductor is the initial voltage V b . 2) After the switch is closed for a long time, what is the energy stored in the inductor? The energy stored in an inductor is given by E = 1 2 LI 2 The maximum current in this circuit is determined by the battery and the resistor. From Ohm’s law, I = V R Thus, E = 1 2 L V R 2 3) The switch in the above diagram is closed after being open a long time. The initial charge on the capacitor is zero. (For each statement select T True, F False). QUESTION: A) In the instant after the switch is closed, the voltage across the capacitor equals the voltage across the battery. B) In the instant after the switch is closed, the voltage across the inductor equals the voltage across the battery. C) A long time after the switch is closed, the voltage across the capacitor equals 1

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the voltage across the battery. D) A long time after the switch is closed, the current through the resistor is zero. ANSWER: A) False, initially capacitors act like wires without resistance, so there is no voltage drop. B) True, there is no current elsewhere in the circuit, so there are no other voltage drops. See (#1). C) True, after a long time a capacitor acts like an infinite resistor, so no current can flow. Thus, the voltage drop must be equal to the battery. D) True, see (C). CAPA is looking for an answer in the form FTTT 4) The next 6 questions refer to this situation: An LR circuit is hooked up to a battery as shown in the figure, with the switch initially open. The resistance in the circuit is R = 110 Ω, the inductance is L = 3 . 40 H and the battery maintains a voltage of E = 30 . 0 V . At time t = 0 the switch is closed. What is the current through the circuit after the switch has been closed for t = 4 . 57 × 10 - 2 s ?
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capa11 - Solution Derivations for Capa#11 Caution The...

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