Exam3_2008Spring_Conflict_Solutions

Exam3_2008Spring_Conflict_Solutions - MASSACHUSETTS...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Conflict Exam Three: Solution 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, the energy in the circuit is stored in 1. The electric field and is decreasing 2. The electric field and is constant 3. The magnetic field and is decreasing 4. The magnetic field and is constant 5. In both the electric and magnetic field and is constant 6. In both the electric and magnetic field and is decreasing Solution: (b). At the instant in question the energy is only stored in the electric field. The energy is constant because there is no energy dissipation through a resistor. Note that because the charge on the capacitor decreases and the current increases, the energy stored in the electric field is decreasing and the energy stored in the magnetic field increases.
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MIT PHYSICS DEPARTMENT ` page 2 Question 2 (5 points): A very long solenoid consisting of N turns has radius R and length d ( d >> R ). Suppose the number of turns is doubled keeping all the other parameters fixed. The self inductance a) remains the same. b) doubles. c) is halved. d) is four times as large. e) is four times as small. Solution: (d). The self inductance is proportional to the number of turns times the magnetic flux through each turn. The magnetic flux through each turn is proportional tot eh magnetic field which is proportional to the number of turns as well. Therefore the self induction is proportional to the square of the number of turns. Hence, if the number of turns is doubles the self inductance is four times as large.
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MIT PHYSICS DEPARTMENT ` page 3 Question 3 (5 points): Consider the RLC circuit below, where at time 0 t = the switch is closed to apply the emf from a battery. The capacitor is initially uncharged. Which of the curves below best approximates the time dependence of the current? (a) (b) ( c ) ( d ) Solution (c): The current begins at zero due to the inductance L and ends at zero due to the capacitance C .
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MIT PHYSICS DEPARTMENT ` page 4 Question 4 (5 points): Consider the plot of the natural logarithm of i ( t ) versus t for a discharging capacitor in an RC circuit. The slope of the line is equal to (a) the time constant (b) minus the time constant (c) the inverse of the time constant (d) minus the inverse of the time constant.
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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_Conflict_Solutions - MASSACHUSETTS...

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