Direct current, resistance, and circuits

1
Direct current, resistance, and circuits

1. At 20.0C, a mainly silicon resistor has a
   resistance of 585 O, and a tungsten resistor has
   a resistance of 752 O. At this temperature, the
   silicon resistor has a temperature coefficient of
   resistivity of -0.070C-1 and the tungsten
   resistor has a coefficient of 0.0050C-1. At what
   temperature will their resistances be equal?
   (16.3C )
2. R1 and R2 are identical. At first, the switch is
   open. When the switch is closed, what happens to
   the power dissipated by R2? Why?
3. You start with a circuit containing only a
   battery and a capacitor. Is the capacitor's
   equilibrium charge affected when you (a) place a
   resistor in series with the capacitor or (b)
   place a resistor in parallel? (c) Explain.

2
circults

1. A battery is modeled as an ideal emf of 18.0 V
   together with an internal resistance. It is in a
   circuit where the only other component is a light
   bulb that is outputting heat and light energy at
   a rate of 75.0 W. The potential difference across
   the battery system is 17.9 V. (a) What is the
   resistance of the hot light bulb? (b) What is the
   internal resistance of the battery? ((a) 4.27 O
   (b) 2.39e-2 O)
2. The potential difference across a battery is
   4.2 V when the current is 3.5 A, and 4.1 V when
   the current is 3.9 A. What is its internal
   resistance?

3
Parallel or serial connections

1. Twelve identical 5.00 µF capacitors are joined
   and used to form the edges of a cube. What is the
   equivalent capacitance between diagonally
   opposite vertices? (6.00e-6 F )

4
Kirchhoffs rules

1. What current flows through the 5.00 O resistor?
   Express your answer to the nearest 0.01 amperes.
   (5.81A).

5
Magnet field

1. The picture shows the paths of some neutral and
   charged particles in a bubble chamber, which
   contains an undisturbed liquid heated above its
   boiling point. The idea is that bubbles begin
   forming on nucleation centers such as surface
   irregularities, or particles moving through the
   liquid. These bubbles allow you to see the trails
   of the particles. Particles enter the chamber
   from the left. A uniform magnetic field is
   directed out of the screen toward you. A certain
   incoming particle (whose trail is not visible)
   splits into 3 other particles, including those
   that follow paths A and B. (a) What is the sign
   of the charge of the particle that follows path
   A? (b) What is the sign of the charge of the
   particle that follows path B? (c) Explain your
   answers. ((a) Negative, (b) Postive)

6
Magnetic field and forces

1. A 5.310-9 kg particle carrying a charge of
   3.210-6 C is accelerated by a potential
   difference of 3,200 V from rest. It then passes
   into a uniform magnetic field of strength
   4.510-3 T. (a) What is the largest force it can
   experience? (b) What is the smallest force it can
   experience?
2. A uranium atom is ionized seven times, losing
   seven electrons in the process. Its resulting
   mass is 3.9010-25 kg and it is given a kinetic
   energy of 3000 eV. If it circles in a magnetic
   field at a radius of 3.00 m, what is the strength
   of the magnetic field? (5.67E-3 T)
3. An alpha particle (m  6.6810-27 kg,
   q  3.2010-19 C) is moving perpendicularly to a
   uniform magnetic field at a speed of
   7.88106 m/s. Because of the force exerted on it
   by the magnetic field, it is accelerating at
   5.671012 m/s2. What is the strength of the
   magnetic field?

7
Magnetic field and current

1. A coaxial cable consists of a central
   current-carrying wire nested concentrically
   inside a conducting cylindrical sheath, which
   carries an equal current in the opposite
   direction. When the cable is in operation, is
   there a magnetic field outside the sheath?
   Explain your answer.
2. A straight horizontal wire carries a current of
   6.50 µA. An electron is moving above the wire a
   direction parallel to it and in the same
   direction as the conventional current in the
   wire, at a constant velocity of 5.41105 m/s.
   Assume that the force of gravity acts on the
   electron and that the electron is moving parallel
   to the Earth's magnetic field, so that the only
   magnetic force on it comes from the field
   generated by the current in the wire. (a) What is
   the magnitude of the upward force that the
   magnetic field must exert on the electron to keep
   it at a constant velocity? (b) How far is the
   electron above the wire?

8
Magnetic field and current

1. An electron is initially moving at a speed of
   1.79e3 m/s directly toward a long wire that has
   2.00 A of current flowing through it. The
   electron is 2.50 m away. What are the direction
   and amount of the force exerted by the magnetic
   field on the electron? (4.58e-23 N, in the same
   direction as the current )

9
Magnetic field and current

1. An alpha particle (two protons and two neutrons,
   with a mass of 6.681027 kg) moves in a circle
   inside a solenoid. The plane of the circle is
   perpendicular to the central axis of the
   solenoid, approximately parallel to the loops,
   and its radius is 5.00 cm. The speed of the
   particle is 2250 m/s. (a) What is the strength of
   the magnetic field inside the solenoid? (b) The
   solenoid carries a current of 10.0 A. How tightly
   wound is the solenoid, in loops per meter?
2. For each of the four diagrams tell whether the
   current is increasing or decreasing based on the
   direction of the current flow and the direction
   of the induced emf.(a) Increasing  
   Decreasing   (b) Increasing   Decreasing   (c)
   Increasing   Decreasing   (d) Increasing  
   Decreasing  

10
Faradays induction law

1. A wire has a resistance of 60.0 ohms, and is bent
   into a square loop with sides of length 15.0 cm.
   The loop is perpendicular to a magnetic field
   which is changing at a rate of 3.00e-3 T/s. What
   is the current induced in the wire? (1.13e-6 A)
2. A series RLC circuit contains an AC generator
   (120 volts rms, frequency  60 Hz), a 35.0 ohm
   resistor, a 1.4910-5 F capacitor, and a 0.0300 H
   inductor. (a) What is the resonant frequency of
   the circuit? Express your answer in Hz. (b)
   Determine the capacitive reactance. (c) Determine
   the inductive reactance. (d) Determine the
   maximum current in the circuit. (e) Determine the
   phase constant. (f) Determine the average power.
   (g) What driving frequency minimizes the circuit
   impedance? (h) What driving frequency maximizes
   the average power consumed?((a) 238 Hz, (b) 178
   O, (c) 11.3 O, (d) 0.996 A, (e) -1.36 rad, (f)
   17.4 W, (g) 238 Hz, (h) 238 Hz)