Download Problem Set 11

Problem Set 11
Due Date: not collected
**Possible 4B CQ on plasma frequency**
An electromagnetic wave consists of intertwined electric and magnetic fields, which jostle
electrically charged particles, such as electrons and ions. We know from experience that a force
does not accelerate all things the same—it is easier to push a lightweight bicycle than a heavy car,
for example. Likewise, electromagnetic waves kick lightweight electrons a lot, whereas heavy
ionized atoms are hardly disturbed. If all of the negatively charged electrons in the plasma are
displaced by a small amount relative to the massive positive ions, the attraction of opposite
charges will pull them back toward their original positions. However, because of their
inertia, the electrons will carry on, overshooting their starting point before being pulled
back again. The result is that the electrons in the plasma oscillate back and forth around
their positions of equilibrium, causing a wave in the plasma itself. This wave oscillates at a
rate known as the “plasma frequency” whose value depends on the density of the plasma. It
is the magnitude of this frequency relative to that of the incoming electromagnetic wave that
determines whether the incoming wave is reflected back in its tracks, as if at a mirror, or
instead continues to travel through the plasma, though modified in intensity and in other
ways.
Chapter 31: Electromagnetic Oscillations & Alternating Current
Exercises & Problems: 35, 37, 43, 46, 74, 79, 81
Question A
Fluorescent lights often use an inductor, called a ballast, to limit the current
through the tubes. Why is it better to use an inductor rather than a resistor for this
purpose?
Question B
In a series LRC circuit, can the instantaneous voltage across the capacitor
exceed the source voltage at the same instant? Can this be true for the
instantaneous voltage across the inductor? Across the resistor? Explain.
Question C
The current in an ac power line charges direction 120 times per second, and it
average value is zero. Explain how it is possible for power to be transmitted in
such a system.
Question D
A lightbulb and a parallel-plate capacitor with air between the plates are
connected in series to an ac source. What happens to the brightness of the bulb
when a dielectric is inserted between the plates of the capacitor? Explain.
Problem 31.35
Consider a series ac RC-circuit with R = 200, C = 70.0 F, fd = 60.0Hz, and m
= 36.0V. What are (a) Z, (b) , and (c) I? (d) Draw a phasor diagram
Answer: 218 , 23.40, 0.165 A
Problem 31.37
Consider a series ac RL-circuit with R = 200, L = 230 mH, fd = 60.0 Hz, and m
= 36.0V. What are (a) Z, (b) , and (c) I? (d) Draw a phasor diagram
Answer: 267 , -41.50, 0.135 A
Problem 31.43
A coil of inductance 88 mH and unknown resistance and a 0.94 μF capacitor are
connected in series with an alternating emf of frequency 930 Hz. If the phase
constant between the applied voltage and the current is 75°, what is the
resistance of the coil?
Answer: 89 
Problem 31.46
The RLC circuit contains two identical
capacitors and two switches. The emf
amplitude is set at 12.0 V, and the driving
frequency is set at 60.0 Hz. With both switches
open, the current leads the emf by 30.9°. With
switch S1 closed and switch S2 still open, the
emf leads the current by 15.0°. With both switches closed, the current amplitude
is 447 mA. What are (a) R, (b) C, and (c) L?
Answer: 100 , 30.6 F, 301mH;
Problem 31.74
A series RLC circuit has a resonant frequency of 6.00 kHz. When it is driven at
8.00 kHz, it has an impedance of 1.00 kΩ and a phase constant of 45°. What are
(a) R, (b) L, and (c) C for this circuit?
Answer: 707 , 21.9F, 32.2 mH;
Problem 31.79
A generator of frequency 3000 Hz drives a series RLC circuit with an emf
amplitude of 120 V. The resistance is 40.0 Ω, the capacitance is 1.60 μF, and the
inductance is 850 μH. What are (a) the phase constant in radians and (b) the
current amplitude? (c) Is the circuit capacitive, inductive, or in resonance?
Answer: -0.405 rad, 2.76 A, capactive
Problem 31.81
A generator with an adjustable frequency of oscillation is wired in series to an
inductor of L = 2.50 mH and a capacitor of C = 3.00 F. At what frequency does
the generator produce the largest possible current amplitude in the circuit?
Answer: 1.84 kHz