Exam3_2008Spring_Solutions

# Exam3_2008Spring_Solutions - MASSACHUSETTS INSTITUTE OF...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Exam Three: Solutions Section I: (25 points) Five Concept Questions. Please circle your answers. Question 1 (5 points): In an LC circuit, the electric and magnetic fields are shown in the figure. At the moment depicted in the figure, a) the current in the circuit is increasing and the charge on the positive plate of the capacitor is decreasing b) the current in the circuit is increasing and the charge on the positive plate of the capacitor is increasing c) the current in the circuit is decreasing and the charge on the positive plate of the capacitor is increasing d) the current in the circuit is decreasing and the charge on the positive plate of the capacitor is decreasing Solution: (a). As the charge on the capacitor decreases the current increases.

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MIT PHYSICS DEPARTMENT ` page 2 Question 2 (5 points): The switch on the circuit shown below is closed at t = 0. Let i denote the current through the resistor. Consider the current ( 0 ) it + = and the current () =∞ . a) (0 )( ) 0 + =− = > . b) ( 0 ) ( ) 0 + = = . c) ) 0 + = < . Solution: (b) At ( 0 ) + = , no current flows through the inductor and the capacitor acts as a short so all the current flows through that branch and is equal to ( 0 ) / V R + == . At , the inductor acts like a short and no current flows through the capacitor so / =∞ = . Thus ( 0 ) ( ) 0 + = = .
MIT PHYSICS DEPARTMENT ` page 3 Question 3 (5 points): A driven RLC circuit uses a lightbulb for the resistor and is driven at 1 Hz, below the resonance frequency of the circuit, so that the flashing of the bulb can easily be seen. If a second light bulb is placed in parallel to the power supply, this bulb will flash: a) At the same times as the first bulb b) Just before the first bulb c) Just after the first bulb d) Not at all Solution: (c). Before the switch is closed the circuit, the circuit is drive below resonance frequency so the current leads the voltage. When the switch is closed, the current and the voltage throught eh second light bulb are in phase lagging behind the current throught eh first light bulb, so the second light bulb goes off just after the first light bulb.

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MIT PHYSICS DEPARTMENT ` page 4 Question 4 (5 points): What is the value of the time constant τ that governs the time dependence of currents and charges in the RC circuit shown below? Assume that all resistors have a common value R of the resistance and that the capacitor is initially charged. a) = (5 / 8) RC . b) (8/5) RC = . c) (3/8) RC = .
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## This note was uploaded on 04/27/2009 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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Exam3_2008Spring_Solutions - MASSACHUSETTS INSTITUTE OF...

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