Exam 24: Capacitance and Dielectrics

LR circuits: Consider the circuit shown in the figure. The battery has emf ε = 25 volts and negligible internal resistance. The inductance is and the resistances are R₁ = 12 Ω and R₂ = 9.0 Ω. Initially the switch S is open and no currents flow. Then the switch is closed. (a) What is the current in the resistor R₁ just after the switch is closed? (b) After leaving the switch closed for a very long time, it is opened again. Just after it is opened, what is the current in R₁?

Motional emf: A conducting bar moves along frictionless conducting rails connected to a 4.00-Ω resistor as shown in the figure. The length of the bar is 1.60 m and a uniform magnetic field of 2.20 T is applied perpendicular to the paper pointing outward, as shown. (a) What is the applied force required to move the bar to the right with a constant speed of 6.00 m/s? (b) At what rate is energy dissipated in the 4.00 Ω resistor?

Motional emf: A conducting bar slides without friction on two parallel horizontal rails that are 50 cm apart and connected by a wire at one end. The resistance of the bar and the rails is constant and equal to 0.10 Ω. A uniform magnetic field is perpendicular to the plane of the rails. A 0.080-N force parallel to the rails is required to keep the bar moving at a constant speed of 0.50 m/s. What is the magnitude of the magnetic field?

Faraday's law: A uniform magnetic field is applied perpendicular to the plane of a 60-turn circular coil with a radius of 6.0 cm and a resistance of 0.60 Ω. If the magnetic field increases uniformly from 0.20 T to 1.8 T in 0.20 s, what is the magnitude of the emf induced in the coil?

Mutual inductance: A 96-mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil's resistance is 9.9 ohms. The mutual inductance of the coil and solenoid is At a given instant, the current in the solenoid is and is decreasing at the rate of At the given instant, what is the magnitude of the induced current in the coil?

Self-inductance: At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

Transformers: An ideal transformer consists of a 500-turn primary coil and a 2000-turn secondary coil. If the current in the secondary is 3.0 A, what is the current in the primary?

Faraday's law: A large magnetic flux change through a coil must induce a greater emf in the coil than a small flux change.

Faraday's law: A coil of 160 turns and area 0.20 m² is placed with its axis parallel to a magnetic field of initial magnitude 0.40 T. The magnetic field changes uniformly from 0.40 T in the +x direction to 0.40 T in the -x direction in 2.0 s. If the resistance of the coil is 16 Ω, at what rate is power generated in the coil?

Lenz's law: A bar magnet is held vertically with its upper end a little bit below the center of a horizontal metal ring. The upper end of the magnet is its north pole, as shown in the figure. The bar magnet is now dropped. An observer views the ring from above its center. To this observer, how will the induced current in the ring behave as the magnet falls?