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Exam 24: Capacitance and Dielectrics

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Question 1

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LR circuits: A series circuit consists of a 0.55-H inductor with internal resistance of 8.0 Ω connected in series with a 4.0-Ω resistor, an open switch, and an ideal 12-V battery. (a) When the switch is closed, what is the initial current through the 4.0-Ω resistor? (b) What is the current through the 4.0-Ω resistor a very long time after the switch is closed?

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(a) 0.00 A (b) 1.0 A

Question 2

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LR circuits: Which of the following statements about inductors are correct? There may be more than one correct choice.

A) When it is connected in a circuit, an inductor always resists having current flow through it.
B) Inductors store energy by building up charge.
C) When an inductor and a resistor are connected in series with a DC battery, the current in the circuit is reduced to zero in one time constant.
D) An inductor always resists any change in the current through it.
E) When an inductor and a resistor are connected in series with a DC battery, the current in the circuit is zero after a very long time.

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Question 3

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Lenz's law: In the figure, a bar magnet moves away from the solenoid. The induced current through the resistor R is

LR circuits: A series LR circuit contains an emf source of having no internal resistance, a resistor, a inductor having no appreciable resistance, and a switch. If the emf across the inductor is of its maximum value after the switch is closed, what is the resistance of the resistor?

Self-inductance: What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T ∙ m/A)

Faraday's law: A closed loop conductor that forms a circle with a radius of is located in a uniform but changing magnetic field. If the maximum emf induced in the loop is what is the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies?

Lenz's law: In the figure, a copper bar is in contact with a pair of parallel metal rails and is in motion with velocity ν. A uniform magnetic field is present pointing downward, as shown. The bar, the rails, and the resistor R are all in the same plane. The induced current through the resistor R is

AC generator: A rectangular coil having N turns and measuring 15 cm by 25 cm is rotating in a uniform 1.6-T magnetic field with a frequency of 75 Hz. The rotation axis is perpendicular to the direction of the field. If the coil develops a sinusoidal emf of maximum value 56.9 V, what is the value of N?

LC circuits: A charged capacitor is connected to an ideal inductor to form an LC circuit with a frequency of oscillation f = 1.6 Hz. At time t = 0 the capacitor is fully charged. At a given instant later the charge on the capacitor is measured to be 3.0 μC and the current in the circuit is equal to 75 μA. What is the maximum charge of the capacitor?

AC generator: The coil in a 50-Hz ac generator has 283 turns, each having an area of 3.0 × 10⁻² m² and is rotated in a uniform 0.12-T magnetic field. What is the peak output voltage of this generator?

Lenz's law: In the figure, two solenoids are side by side. The switch S, initially open, is closed. The induced current through the resistor R is

Lenz's law: The figure shows a bar magnet moving vertically upward toward a horizontal coil. The poles of the bar magnets are labeled X and Y. As the bar magnet approaches the coil it induces an electric current in the direction indicated on the figure (counter-clockwise as viewed from above) . What are the correct polarities of the magnet?

LR circuits: A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, an open switch, and a 9.0-V ideal power source. After the switch is closed, what is the maximum power delivered by the power supply?

Transformers: In a transformer, how many turns are necessary in a 230-V primary if the 24-V secondary has 100 turns?

LC circuits: A charged capacitor is connected to an ideal inductor. At time t = 0, the charge on the capacitor is equal to 6.00 μC. At time t = 2.00 ms the charge on the capacitor is zero for the first time. What is the amplitude of the current at that same instant?

Transformers: The primary coil of a transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is 230 V, what voltage is present in its secondary coil?

Energy in an inductor: At a certain instant the current flowing through a 5.0-H inductor is 3.0 A. If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s, how fast is the current changing?

Mutual inductance: The mutual inductance between two coils is 10.0 mH. The current in the first coil changes uniformly from 2.70 A to 5.00 A in 0.160 s. If the second coil has a resistance of 0.600 Ω, what is the magnitude of the induced current in the second coil?

Energy in an inductor: An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ₀ = 4π × 10^-7 T ∙ m/A)

Energy density: What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T ∙ m/A)