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1308 E&M
Direct current, resistance, and circuits
1.
At 20.0°C, a mainly silicon resistor has a resistance of 585 Ω, and a
tungsten resistor has a resistance of 752 Ω. At this temperature, the
silicon resistor has a temperature coefficient of resistivity of −0.070°C−1
and the tungsten resistor has a coefficient of 0.0050°C−1. At what
temperature will their resistances be equal? (16.3°C )
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.
1308 E&M
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 Ω (b) 2.39e−2 Ω)
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?
1308 E&M
1.
Parallel or serial connections
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 )
1308 E&M
1.
Kirchhoff’s rules
What current flows through the 5.00 Ω resistor? Express your answer to
the nearest 0.01 amperes. (5.81A).
1308 E&M
1.
Magnet field
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)
1308 E&M
Magnetic field and forces
1.
A 5.3×10−9 kg particle carrying a charge of 3.2×10−6 C is accelerated by a
potential difference of 3,200 V from rest. It then passes into a uniform
magnetic field of strength 4.5×10−3 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 3.90×10−25 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 = 6.68×10−27 kg, q = 3.20×10−19 C) is moving
perpendicularly to a uniform magnetic field at a speed of 7.88×106 m/s.
Because of the force exerted on it by the magnetic field, it is accelerating
at 5.67×1012 m/s2. What is the strength of the magnetic field?
1308 E&M
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 5.41×105 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?
1308 E&M
1.
Magnetic field and current
An electron is initially moving at a speed of 1.79e+3 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 )
Magnetic field and current
1308 E&M
1.
An alpha particle (two protons and two neutrons, with a mass of 6.68×10–
27 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
(b) Increasing
(c) Increasing
(d) Increasing
Decreasing
Decreasing
Decreasing
Decreasing
1308 E&M
Faraday’s 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 1.49×10−5 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 Ω, (c) 11.3 Ω, (d) 0.996 A, (e) −1.36 rad, (f) 17.4 W, (g) 238 Hz, (h) 238 Hz)